Class Measures

Set of statistics measures, such as Mean(Double[]), Variance(Double[]) and StandardDeviation(Double[], Boolean).

Inheritance

System.Object

Measures

Namespace: ISynergy.Framework.Mathematics.Statistics

Assembly: ISynergy.Framework.Mathematics.dll

Syntax

public static class Measures : object

Methods

View Source

ContraHarmonicMean(Double[])

Computes the contraharmonic mean of the given values.

Declaration

public static double ContraHarmonicMean(double[] values)

Parameters

Type	Name	Description
System.Double[]	values	A unsigned short array containing the vector members.

Returns

Type	Description
System.Double	The contraharmonic mean of the given data.

View Source

ContraHarmonicMean(Double[], Int32)

Computes the contraharmonic mean of the given values.

Declaration

public static double ContraHarmonicMean(double[] values, int order)

Parameters

Type	Name	Description
System.Double[]	values	A unsigned short array containing the vector members.
System.Int32	order	The order of the harmonic mean. Default is 1.

Returns

Type	Description
System.Double	The contraharmonic mean of the given data.

View Source

Correlation(Double[][])

Calculates the correlation matrix for a matrix of samples.

Declaration

public static double[][] Correlation(this double[][] matrix)

Parameters

Type	Name	Description
System.Double[][]	matrix	A multi-dimensional array containing the matrix values.

Returns

Type	Description
System.Double[][]	The correlation matrix.

Remarks

In statistics and probability theory, the correlation matrix is the same as the covariance matrix of the standardized random variables.

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Correlation(Double[][], Double[], Double[])

Calculates the correlation matrix for a matrix of samples.

Declaration

public static double[][] Correlation(this double[][] matrix, double[] means, double[] standardDeviations)

Parameters

Type	Name	Description
System.Double[][]	matrix	A multi-dimensional array containing the matrix values.
System.Double[]	means	The mean value of the given values, if already known.
System.Double[]	standardDeviations	The values' standard deviation vector, if already known.

Returns

Type	Description
System.Double[][]	The correlation matrix.

Remarks

In statistics and probability theory, the correlation matrix is the same as the covariance matrix of the standardized random variables.

View Source

Correlation(Double[,])

Calculates the correlation matrix for a matrix of samples.

Declaration

public static double[, ] Correlation(this double[, ] matrix)

Parameters

Type	Name	Description
System.Double[,]	matrix	A multi-dimensional array containing the matrix values.

Returns

Type	Description
System.Double[,]	The correlation matrix.

Remarks

In statistics and probability theory, the correlation matrix is the same as the covariance matrix of the standardized random variables.

View Source

Correlation(Double[,], Double[], Double[])

Calculates the correlation matrix for a matrix of samples.

Declaration

public static double[, ] Correlation(this double[, ] matrix, double[] means, double[] standardDeviations)

Parameters

Type	Name	Description
System.Double[,]	matrix	A multi-dimensional array containing the matrix values.
System.Double[]	means	The mean value of the given values, if already known.
System.Double[]	standardDeviations	The values' standard deviation vector, if already known.

Returns

Type	Description
System.Double[,]	The correlation matrix.

Remarks

In statistics and probability theory, the correlation matrix is the same as the covariance matrix of the standardized random variables.

View Source

Covariance(Double[], Double, Double[], Double, Boolean)

Computes the Covariance between two arrays of values.

Declaration

public static double Covariance(this double[] vector1, double mean1, double[] vector2, double mean2, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[]	vector1	A number array containing the first vector elements.
System.Double	mean1	The mean value of `vector1`, if known.
System.Double[]	vector2	A number array containing the second vector elements.
System.Double	mean2	The mean value of `vector2`, if known.
System.Boolean	unbiased	Pass true to compute the sample variance; or pass false to compute the population variance. See remarks for more details.

Returns

Type	Description
System.Double	The variance of the given data.

Remarks

Setting unbiased to true will make this method compute the variance σ² using the sample variance, which is an unbiased estimator of the true population variance. Setting this parameter to true will thus compute σ² using the following formula:

                      N
   σ² = 1 / (N - 1)  ∑   (x_i − μ)²
                      i=1

Setting unbiased to false will assume the given values already represent the whole population, and will compute the population variance using the formula:

                      N
   σ² =   (1 / N)    ∑   (x_i − μ)²
                      i=1

View Source

Covariance(Double[], Double[], Boolean)

Computes the Covariance between two arrays of values.

Declaration

public static double Covariance(this double[] vector1, double[] vector2, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[]	vector1	A number array containing the first vector elements.
System.Double[]	vector2	A number array containing the second vector elements.
System.Boolean	unbiased	Pass true to compute the sample variance; or pass false to compute the population variance. See remarks for more details.

Returns

Type	Description
System.Double	The variance of the given data.

Remarks

                      N
   σ² = 1 / (N - 1)  ∑   (x_i − μ)²
                      i=1

Setting unbiased to false will assume the given values already represent the whole population, and will compute the population variance using the formula:

                      N
   σ² =   (1 / N)    ∑   (x_i − μ)²
                      i=1

View Source

Covariance(Double[][])

Calculates the covariance matrix of a sample matrix.

Declaration

public static double[][] Covariance(this double[][] matrix)

Parameters

Type	Name	Description
System.Double[][]	matrix	A number multi-dimensional array containing the matrix values.

Returns

Type	Description
System.Double[][]	The covariance matrix.

Remarks

In statistics and probability theory, the covariance matrix is a matrix of covariances between elements of a vector. It is the natural generalization to higher dimensions of the concept of the variance of a scalar-valued random variable.

View Source

Covariance(Double[][], Double[])

Calculates the covariance matrix of a sample matrix.

Declaration

public static double[][] Covariance(this double[][] matrix, double[] means)

Parameters

Type	Name	Description
System.Double[][]	matrix	A number multi-dimensional array containing the matrix values.
System.Double[]	means	The mean value of the given values, if already known.

Returns

Type	Description
System.Double[][]	The covariance matrix.

Remarks

View Source

Covariance(Double[][], Int32)

Calculates the covariance matrix of a sample matrix.

Declaration

public static double[][] Covariance(this double[][] matrix, int dimension)

Parameters

Type	Name	Description
System.Double[][]	matrix	A number multi-dimensional array containing the matrix values.
System.Int32	dimension	The dimension of the matrix to consider as observations. Pass 0 if the matrix has observations as rows and variables as columns, pass 1 otherwise. Default is 0.

Returns

Type	Description
System.Double[][]	The covariance matrix.

Remarks

View Source

Covariance(Double[,])

Calculates the covariance matrix of a sample matrix.

Declaration

public static double[, ] Covariance(this double[, ] matrix)

Parameters

Type	Name	Description
System.Double[,]	matrix	A number multi-dimensional array containing the matrix values.

Returns

Type	Description
System.Double[,]	The covariance matrix.

Remarks

View Source

Covariance(Double[,], Double[])

Calculates the covariance matrix of a sample matrix.

Declaration

public static double[, ] Covariance(this double[, ] matrix, double[] means)

Parameters

Type	Name	Description
System.Double[,]	matrix	A number multi-dimensional array containing the matrix values.
System.Double[]	means	The mean value of the given values, if already known.

Returns

Type	Description
System.Double[,]	The covariance matrix.

Remarks

View Source

Covariance(Double[,], Int32)

Calculates the covariance matrix of a sample matrix.

Declaration

public static double[, ] Covariance(this double[, ] matrix, int dimension)

Parameters

Type	Name	Description
System.Double[,]	matrix	A number multi-dimensional array containing the matrix values.
System.Int32	dimension	The dimension of the matrix to consider as observations. Pass 0 if the matrix has observations as rows and variables as columns, pass 1 otherwise. Default is 0.

Returns

Type	Description
System.Double[,]	The covariance matrix.

Remarks

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Entropy(IList<Int32>, Int32)

Computes the entropy for the given values.

Declaration

public static double Entropy(IList<int> values, int classes)

Parameters

Type	Name	Description
IList<System.Int32>	values	An array of integer symbols.
System.Int32	classes	The number of distinct classes.

Returns

Type	Description
System.Double	The evaluated entropy.

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Entropy(IList<Int32>, Int32, Int32)

Computes the entropy for the given values.

Declaration

public static double Entropy(IList<int> values, int startValue, int endValue)

Parameters

Type	Name	Description
IList<System.Int32>	values	An array of integer symbols.
System.Int32	startValue	The starting symbol.
System.Int32	endValue	The ending symbol.

Returns

Type	Description
System.Double	The evaluated entropy.

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Entropy(Boolean, Boolean)

Computes the entropy function between an expected value and a predicted value.

Declaration

public static double Entropy(bool expected, bool predicted)

Parameters

Type	Name	Description
System.Boolean	expected
System.Boolean	predicted

Returns

Type	Description
System.Double

View Source

Entropy(Boolean, Double)

Computes the entropy function between an expected value and a predicted value between 0 and 1.

Declaration

public static double Entropy(bool expected, double predicted)

Parameters

Type	Name	Description
System.Boolean	expected
System.Double	predicted

Returns

Type	Description
System.Double

View Source

Entropy(Double[])

Computes the entropy for the given values.

Declaration

public static double Entropy(this double[] values)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector values.

Returns

Type	Description
System.Double	The calculated entropy for the given values.

View Source

Entropy(Double[], Func<Double, Double>)

Computes the entropy function for a set of numerical values in a given Probability Density Function (pdf).

Declaration

public static double Entropy(this double[] values, Func<double, double> pdf)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector values.
Func<System.Double, System.Double>	pdf	A probability distribution function.

Returns

Type	Description
System.Double	The distribution's entropy for the given values.

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Entropy(Double[], NumericRange)

Computes the entropy for the given values.

Declaration

public static double Entropy(double[] values, NumericRange valueRange)

Parameters

Type	Name	Description
System.Double[]	values	An array of integer symbols.
NumericRange	valueRange	The range of symbols.

Returns

Type	Description
System.Double	The evaluated entropy.

View Source

Entropy(Double[], Double)

Computes the entropy for the given values.

Declaration

public static double Entropy(this double[] values, double eps = null)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector values.
System.Double	eps	A small constant to avoid s in case the there is a zero between the given `values`.

Returns

Type	Description
System.Double	The calculated entropy for the given values.

View Source

Entropy(Double[], Double, Double)

Computes the entropy for the given values.

Declaration

public static double Entropy(double[] values, double startValue, double endValue)

Parameters

Type	Name	Description
System.Double[]	values	An array of integer symbols.
System.Double	startValue	The starting symbol.
System.Double	endValue	The ending symbol.

Returns

Type	Description
System.Double	The evaluated entropy.

View Source

Entropy(Double[], Double[], Func<Double, Double>)

Computes the entropy function for a set of numerical values in a given Probability Density Function (pdf).

Declaration

public static double Entropy(this double[] values, double[] weights, Func<double, double> pdf)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector values.
System.Double[]	weights	The importance for each sample.
Func<System.Double, System.Double>	pdf	A probability distribution function.

Returns

Type	Description
System.Double	The distribution's entropy for the given values.

View Source

Entropy(Double[,])

Computes the entropy for the given values.

Declaration

public static double Entropy(this double[, ] values)

Parameters

Type	Name	Description
System.Double[,]	values	A number matrix containing the matrix values.

Returns

Type	Description
System.Double	The calculated entropy for the given values.

View Source

Entropy(Double[,], Double)

Computes the entropy for the given values.

Declaration

public static double Entropy(this double[, ] values, double eps = null)

Parameters

Type	Name	Description
System.Double[,]	values	A number matrix containing the matrix values.
System.Double	eps	A small constant to avoid s in case the there is a zero between the given `values`.

Returns

Type	Description
System.Double	The calculated entropy for the given values.

View Source

Entropy(Int32[], Int32)

Computes the entropy for the given values.

Declaration

public static double Entropy(int[] values, int classes)

Parameters

Type	Name	Description
System.Int32[]	values	An array of integer symbols.
System.Int32	classes	The number of distinct classes.

Returns

Type	Description
System.Double	The evaluated entropy.

View Source

ExponentialWeightedCovariance(Double[][], Double, Boolean)

Calculates the exponentially weighted covariance matrix.

Declaration

public static double[, ] ExponentialWeightedCovariance(this double[][] matrix, double alpha = null, bool unbiased = false)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix of observations whose EW covariance matrix will be calculated. It is assumed that the matrix is ordered with the most recent observations at the bottom of the matrix.
System.Double	alpha	The weighting to be applied to the calculation. A higher alpha discounts older observations faster. Alpha must be between 0 and 1 (inclusive).
System.Boolean	unbiased	Use a standard estimation bias correction.

Returns

Type	Description
System.Double[,]	Returns a vector containing the exponentially weighted average of the columns of the given matrix.

Examples

The following example shows how to compute the EW covariance matrix.

View Source

ExponentialWeightedCovariance(Double[][], Int32, Double, Boolean)

Calculates the exponentially weighted covariance matrix.

Declaration

public static double[, ] ExponentialWeightedCovariance(this double[][] matrix, int window, double alpha = null, bool unbiased = false)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix of observations whose EW covariance matrix will be calculated. It is assumed that the matrix is ordered with the most recent observations at the bottom of the matrix.
System.Int32	window	The number of rows to be used in the calculation.
System.Double	alpha	The weighting to be applied to the calculation. A higher alpha discounts older observations faster. Alpha must be between 0 and 1 (inclusive).
System.Boolean	unbiased	Use a standard estimation bias correction.

Returns

Type	Description
System.Double[,]	Returns a vector containing the exponentially weighted average of the columns of the given matrix.

Examples

The following example shows how to compute the EW covariance matrix.

View Source

ExponentialWeightedMean(Double[], Double)

Calculates the exponentially weighted mean.

Declaration

public static double ExponentialWeightedMean(this double[] values, double alpha = null)

Parameters

Type	Name	Description
System.Double[]	values	A vector of observations whose EW mean will be calculated. It is assumed that the vector is ordered with the most recent observations at the end of the vector (and the oldest observations at the start).
System.Double	alpha	The weighting to be applied to the calculation. A higher alpha discounts older observations faster. Alpha must be between 0 and 1 (inclusive).

Returns

Type	Description
System.Double	Returns a giving the exponentially weighted average of the vector.

Examples

The following example shows how to compute the EW mean.

View Source

ExponentialWeightedMean(Double[], Int32, Double)

Calculates the exponentially weighted mean.

Declaration

public static double ExponentialWeightedMean(this double[] values, int window, double alpha = null)

Parameters

Type	Name	Description
System.Double[]	values	A vector of observations whose EW mean will be calculated. It is assumed that the vector is ordered with the most recent observations at the end of the vector (and the oldest observations at the start).
System.Int32	window	The number of samples to be used in the calculation.
System.Double	alpha	The weighting to be applied to the calculation. A higher alpha discounts older observations faster. Alpha must be between 0 and 1 (inclusive).

Returns

Type	Description
System.Double	Returns a giving the exponentially weighted average of the vector.

Examples

The following example shows how to compute the EW mean.

View Source

ExponentialWeightedMean(Double[][], Double)

Calculates the exponentially weighted mean vector.

Declaration

public static double[] ExponentialWeightedMean(this double[][] matrix, double alpha = null)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix of observations whose EW mean vector will be calculated. It is assumed that the matrix is ordered with the most recent observations at the bottom of the matrix.
System.Double	alpha	The weighting to be applied to the calculation. A higher alpha discounts older observations faster. Alpha must be between 0 and 1 (inclusive).

Returns

Type	Description
System.Double[]	Returns a vector containing the exponentially weighted average of the columns of the given matrix.

Examples

The following example shows how to compute the EW mean.

View Source

ExponentialWeightedMean(Double[][], Int32, Double)

Calculates the exponentially weighted mean vector.

Declaration

public static double[] ExponentialWeightedMean(this double[][] matrix, int window, double alpha = null)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix of observations whose EW mean vector will be calculated. It is assumed that the matrix is ordered with the most recent observations at the bottom of the matrix.
System.Int32	window	The number of rows to be used in the calculation.
System.Double	alpha	The weighting to be applied to the calculation. A higher alpha discounts older observations faster. Alpha must be between 0 and 1 (inclusive).

Returns

Type	Description
System.Double[]	Returns a vector containing the exponentially weighted average of the columns of the given matrix.

Examples

The following example shows how to compute the EW mean.

View Source

ExponentialWeightedVariance(Double[], Double, Boolean)

Calculates the exponentially weighted variance.

Declaration

public static double ExponentialWeightedVariance(this double[] values, double alpha = null, bool unbiased = false)

Parameters

Type	Name	Description
System.Double[]	values	A vector of observations whose EW variance will be calculated. It is assumed that the vector is ordered with the most recent observations at the end of the vector (and the oldest observations at the start).
System.Double	alpha	The weighting to be applied to the calculation. A higher alpha discounts older observations faster. Alpha must be between 0 and 1 (inclusive).
System.Boolean	unbiased	Use a standard estimation bias correction.

Returns

Type	Description
System.Double	Returns a giving the exponentially weighted variance.

Examples

The following example shows how to compute the EW variance.

View Source

ExponentialWeightedVariance(Double[], Int32, Double, Boolean)

Calculates the exponentially weighted variance.

Declaration

public static double ExponentialWeightedVariance(this double[] values, int window, double alpha = null, bool unbiased = false)

Parameters

Type	Name	Description
System.Double[]	values	A vector of observations whose EW variance will be calculated. It is assumed that the vector is ordered with the most recent observations at the end of the vector (and the oldest observations at the start).
System.Int32	window	The number of samples to be used in the calculation.
System.Double	alpha	The weighting to be applied to the calculation. A higher alpha discounts older observations faster. Alpha must be between 0 and 1 (inclusive).
System.Boolean	unbiased	Use a standard estimation bias correction.

Returns

Type	Description
System.Double	Returns a giving the exponentially weighted variance.

Examples

The following example shows how to compute the EW variance.

View Source

GeometricMean(Double[])

Computes the Geometric mean of the given values.

Declaration

public static double GeometricMean(this double[] values)

Parameters

Type	Name	Description
System.Double[]	values	A double array containing the vector members.

Returns

Type	Description
System.Double	The geometric mean of the given data.

View Source

GeometricMean(Int32[])

Computes the geometric mean of the given values.

Declaration

public static double GeometricMean(this int[] values)

Parameters

Type	Name	Description
System.Int32[]	values	A double array containing the vector members.

Returns

Type	Description
System.Double	The geometric mean of the given data.

View Source

GetHistogramRange(Int32[], Double)

Get range around median of an histogram containing specified percentage of values.

Declaration

public static NumericRange GetHistogramRange(this int[] values, double percent)

Parameters

Type	Name	Description
System.Int32[]	values	Histogram array.
System.Double	percent	Values percentage around median.

Returns

Type	Description
NumericRange	Returns the range which contains specified percentage of values.

Remarks

The input array is treated as histogram, i.e. its indexes are treated as values of stochastic function, but array values are treated as "probabilities" (total amount of hits).

The method calculates range of stochastic variable, which summary probability comprises the specified percentage of histogram's hits.

View Source

GrandMean(Double[], Int32[])

Computes the (weighted) grand mean of a set of samples.

Declaration

public static double GrandMean(double[] means, int[] samples)

Parameters

Type	Name	Description
System.Double[]	means	A double array containing the sample means.
System.Int32[]	samples	A integer array containing the sample's sizes.

Returns

Type	Description
System.Double	The grand mean of the samples.

View Source

HistogramEntropy(Int32[])

Calculate entropy value of an histogram.

Declaration

public static double HistogramEntropy(this int[] values)

Parameters

Type	Name	Description
System.Int32[]	values	Histogram array.

Returns

Type	Description
System.Double	Returns entropy value of the specified histogram array.

Remarks

The input array is treated as histogram, i.e. its indexes are treated as values of stochastic function, but array values are treated as "probabilities" (total amount of hits).

View Source

HistogramMax(Int32[])

Gets the maximum value in the histogram.

Declaration

public static int HistogramMax(this int[] values)

Parameters

Type	Name	Description
System.Int32[]	values	Histogram array.

Returns

Type	Description
System.Int32	The maximum value in the histogram.

View Source

HistogramMean(Int32[])

Calculate mean value of an histogram.

Declaration

public static double HistogramMean(this int[] values)

Parameters

Type	Name	Description
System.Int32[]	values	Histogram array.

Returns

Type	Description
System.Double	Returns mean value.

Remarks

The input array is treated as histogram, i.e. its indexes are treated as values of stochastic function, but array values are treated as "probabilities" (total amount of hits).

View Source

HistogramMedian(Int32[])

Calculate median value of an histogram.

Declaration

public static int HistogramMedian(this int[] values)

Parameters

Type	Name	Description
System.Int32[]	values	Histogram array.

Returns

Type	Description
System.Int32	Returns value of median.

Remarks

The input array is treated as histogram, i.e. its indexes are treated as values of stochastic function, but array values are treated as "probabilities" (total amount of hits).

note

The median value is calculated accumulating histogram's values starting from the left point until the sum reaches 50% of histogram's sum.

View Source

HistogramMin(Int32[])

Gets the minimum value in the histogram.

Declaration

public static int HistogramMin(this int[] values)

Parameters

Type	Name	Description
System.Int32[]	values	Histogram array.

Returns

Type	Description
System.Int32	The minimum value in the histogram.

View Source

HistogramMode(Int32[])

Calculate mode value of an histogram.

Declaration

public static int HistogramMode(this int[] values)

Parameters

Type	Name	Description
System.Int32[]	values	Histogram array.

Returns

Type	Description
System.Int32	Returns mode value of the histogram array.

Remarks

The input array is treated as histogram, i.e. its indexes are treated as values of stochastic function, but array values are treated as "probabilities" (total amount of hits).

note

Returns the minimum mode value if the specified histogram is multimodal.

View Source

HistogramStandardDeviation(Int32[])

Calculate standard deviation of an histogram.

Declaration

public static double HistogramStandardDeviation(this int[] values)

Parameters

Type	Name	Description
System.Int32[]	values	Histogram array.

Returns

Type	Description
System.Double	Returns value of standard deviation.

Remarks

The input array is treated as histogram, i.e. its indexes are treated as values of stochastic function, but array values are treated as "probabilities" (total amount of hits).

View Source

HistogramStandardDeviation(Int32[], Double)

Calculate standard deviation of an histogram.

Declaration

public static double HistogramStandardDeviation(this int[] values, double mean)

Parameters

Type	Name	Description
System.Int32[]	values	Histogram array.
System.Double	mean	Mean value of the histogram.

Returns

Type	Description
System.Double	Returns value of standard deviation.

Remarks

The input array is treated as histogram, i.e. its indexes are treated as values of stochastic function, but array values are treated as "probabilities" (total amount of hits).

The method is an equivalent to the HistogramStandardDeviation(Int32[]) method, but it relies on the passed mean value, which is previously calculated using HistogramMean(Int32[]) method.

View Source

HistogramSum(Int32[])

Calculates the total number of samples in a histogram.

Declaration

public static long HistogramSum(this int[] values)

Parameters

Type	Name	Description
System.Int32[]	values	The histogram array.

Returns

Type	Description
System.Int64	The total number of samples in the histogram.

View Source

Kurtosis(Double[], Boolean)

Computes the Kurtosis for the given values.

Declaration

public static double Kurtosis(this double[] values, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector values.
System.Boolean	unbiased	True to compute the unbiased estimate of the population kurtosis, false otherwise. Default is true (compute the unbiased estimator).

Returns

Type	Description
System.Double	The kurtosis of the given data.

Remarks

The framework uses the same definition used by default in SAS and SPSS.

View Source

Kurtosis(Double[], Double, Boolean)

Computes the Kurtosis for the given values.

Declaration

public static double Kurtosis(this double[] values, double mean, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector values.
System.Double	mean	The values' mean, if already known.
System.Boolean	unbiased	True to compute the unbiased estimate of the population kurtosis, false otherwise. Default is true (compute the unbiased estimator).

Returns

Type	Description
System.Double	The kurtosis of the given data.

Remarks

The framework uses the same definition used by default in SAS and SPSS.

View Source

Kurtosis(Double[][], Boolean)

Computes the Kurtosis vector for the given matrix.

Declaration

public static double[] Kurtosis(this double[][] matrix, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[][]	matrix	A number multi-dimensional array containing the matrix values.
System.Boolean	unbiased	True to compute the unbiased estimate of the population kurtosis, false otherwise. Default is true (compute the unbiased estimator).

Returns

Type	Description
System.Double[]	The kurtosis vector of the given data.

Remarks

The framework uses the same definition used by default in SAS and SPSS.

View Source

Kurtosis(Double[][], Double[], Boolean)

Computes the Kurtosis vector for the given matrix.

Declaration

public static double[] Kurtosis(this double[][] matrix, double[] means, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[][]	matrix	A number multi-dimensional array containing the matrix values.
System.Double[]	means	The mean value of the given values, if already known.
System.Boolean	unbiased	True to compute the unbiased estimate of the population kurtosis, false otherwise. Default is true (compute the unbiased estimator).

Returns

Type	Description
System.Double[]	The kurtosis vector of the given data.

Remarks

The framework uses the same definition used by default in SAS and SPSS.

View Source

Kurtosis(Double[,], Boolean)

Computes the Kurtosis vector for the given matrix.

Declaration

public static double[] Kurtosis(this double[, ] matrix, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[,]	matrix	A number multi-dimensional array containing the matrix values.
System.Boolean	unbiased	True to compute the unbiased estimate of the population kurtosis, false otherwise. Default is true (compute the unbiased estimator).

Returns

Type	Description
System.Double[]	The kurtosis vector of the given data.

Remarks

The framework uses the same definition used by default in SAS and SPSS.

View Source

Kurtosis(Double[,], Double[], Boolean)

Computes the sample Kurtosis vector for the given matrix.

Declaration

public static double[] Kurtosis(this double[, ] matrix, double[] means, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[,]	matrix	A number multi-dimensional array containing the matrix values.
System.Double[]	means	The mean value of the given values, if already known.
System.Boolean	unbiased	True to compute the unbiased estimate of the population kurtosis, false otherwise. Default is true (compute the unbiased estimator).

Returns

Type	Description
System.Double[]	The sample kurtosis vector of the given data.

Remarks

The framework uses the same definition used by default in SAS and SPSS.

View Source

LogGeometricMean(Double[])

Computes the log geometric mean of the given values.

Declaration

public static double LogGeometricMean(this double[] values)

Parameters

Type	Name	Description
System.Double[]	values	A double array containing the vector members.

Returns

Type	Description
System.Double	The log geometric mean of the given data.

View Source

LogGeometricMean(Int32[])

Computes the log geometric mean of the given values.

Declaration

public static double LogGeometricMean(this int[] values)

Parameters

Type	Name	Description
System.Int32[]	values	A double array containing the vector members.

Returns

Type	Description
System.Double	The log geometric mean of the given data.

View Source

LowerQuartile(Double[], Boolean, QuantileMethod, Boolean)

Computes the lower quartile (Q1) for the given data.

Declaration

public static double LowerQuartile(this double[] values, bool alreadySorted = false, QuantileMethod type = default(QuantileMethod), bool inPlace = false)

Parameters

Type	Name	Description
System.Double[]	values	An integer array containing the vector members.
System.Boolean	alreadySorted	A boolean parameter informing if the given values have already been sorted.
QuantileMethod	type	The quartile definition that should be used. See QuantileMethod for datails.
System.Boolean	inPlace	Pass true if the method is allowed to sort `values` in place, overwriting the its original order.

Returns

Type	Description
System.Double	The first quartile of the given data.

View Source

Mean(Double[])

Computes the mean of the given values.

Declaration

public static double Mean(this double[] values)

Parameters

Type	Name	Description
System.Double[]	values	A double array containing the vector members.

Returns

Type	Description
System.Double	The mean of the given data.

View Source

Mean(Double[][])

Computes the mean value across all dimensions of the given matrix.

Declaration

public static double Mean(this double[][] matrix)

Parameters

Type	Name	Description
System.Double[][]	matrix

Returns

Type	Description
System.Double

View Source

Mean(Double[][], Double[])

Calculates the matrix Mean vector.

Declaration

public static double[] Mean(this double[][] matrix, double[] sums)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose means will be calculated.
System.Double[]	sums	The sum vector containing already calculated sums for each column of the matrix.

Returns

Type	Description
System.Double[]	Returns a vector containing the means of the given matrix.

View Source

Mean(Double[][], Int32)

Calculates the matrix Mean vector.

Declaration

public static double[] Mean(this double[][] matrix, int dimension)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose means will be calculated.
System.Int32	dimension	The dimension along which the means will be calculated. Pass 0 to compute a row vector containing the mean of each column, or 1 to compute a column vector containing the mean of each row. Default value is 0.

Returns

Type	Description
System.Double[]	Returns a vector containing the means of the given matrix.

Examples

double[][] matrix = 
{
    new double[] { 2, -1.0, 5 },
    new double[] { 7,  0.5, 9 },
};

// column means are equal to (4.5, -0.25, 7.0)
double[] colMeans = Stats.Mean(matrix, 0);

// row means are equal to (2.0, 5.5)
double[] rowMeans = Stats.Mean(matrix, 1);

View Source

Mean(Double[,])

Computes the mean value across all dimensions of the given matrix.

Declaration

public static double Mean(this double[, ] matrix)

Parameters

Type	Name	Description
System.Double[,]	matrix

Returns

Type	Description
System.Double

View Source

Mean(Double[,], Double[])

Calculates the matrix Mean vector.

Declaration

public static double[] Mean(this double[, ] matrix, double[] sums)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose means will be calculated.
System.Double[]	sums	The sum vector containing already calculated sums for each column of the matrix.

Returns

Type	Description
System.Double[]	Returns a vector containing the means of the given matrix.

View Source

Mean(Double[,], Int32)

Calculates the matrix Mean vector.

Declaration

public static double[] Mean(this double[, ] matrix, int dimension)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose means will be calculated.
System.Int32	dimension	The dimension along which the means will be calculated. Pass 0 to compute a row vector containing the mean of each column, or 1 to compute a column vector containing the mean of each row. Default value is 0.

Returns

Type	Description
System.Double[]	Returns a vector containing the means of the given matrix.

Examples

double[,] matrix = 
{
   { 2, -1.0, 5 },
   { 7,  0.5, 9 },
};

// column means are equal to (4.5, -0.25, 7.0)
double[] colMeans = Stats.Mean(matrix, 0);

// row means are equal to (2.0, 5.5)
double[] rowMeans = Stats.Mean(matrix, 1);

View Source

Mean(Int32[])

Computes the mean of the given values.

Declaration

public static double Mean(this int[] values)

Parameters

Type	Name	Description
System.Int32[]	values	An integer array containing the vector members.

Returns

Type	Description
System.Double	The mean of the given data.

View Source

Mean(Single[])

Computes the mean of the given values.

Declaration

public static float Mean(this float[] values)

Parameters

Type	Name	Description
System.Single[]	values	A float array containing the vector members.

Returns

Type	Description
System.Single	The mean of the given data.

View Source

Mean(UInt16[])

Computes the mean of the given values.

Declaration

public static double Mean(this ushort[] values)

Parameters

Type	Name	Description
System.UInt16[]	values	A unsigned short array containing the vector members.

Returns

Type	Description
System.Double	The mean of the given data.

View Source

Median(Double[], Boolean, QuantileMethod, Boolean)

Computes the Median of the given values.

Declaration

public static double Median(this double[] values, bool alreadySorted = false, QuantileMethod type = default(QuantileMethod), bool inPlace = false)

Parameters

Type	Name	Description
System.Double[]	values	An integer array containing the vector members.
System.Boolean	alreadySorted	A boolean parameter informing if the given values have already been sorted.
QuantileMethod	type	The quartile definition that should be used. See QuantileMethod for datails.
System.Boolean	inPlace	Pass true if the method is allowed to sort `values` in place, overwriting the its original order.

Returns

Type	Description
System.Double	The median of the given data.

View Source

Median(Double[][], QuantileMethod)

Calculates the matrix Medians vector.

Declaration

public static double[] Median(this double[][] matrix, QuantileMethod type = default(QuantileMethod))

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose medians will be calculated.
QuantileMethod	type	The quartile definition that should be used. See QuantileMethod for datails.

Returns

Type	Description
System.Double[]	Returns a vector containing the medians of the given matrix.

View Source

Median(Double[,], QuantileMethod)

Calculates the matrix Medians vector.

Declaration

public static double[] Median(this double[, ] matrix, QuantileMethod type = default(QuantileMethod))

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose medians will be calculated.
QuantileMethod	type	The quartile definition that should be used. See QuantileMethod for datails.

Returns

Type	Description
System.Double[]	Returns a vector containing the medians of the given matrix.

View Source

Median(Int32[], Boolean, QuantileMethod, Boolean)

Computes the Median of the given values.

Declaration

public static double Median(this int[] values, bool alreadySorted = false, QuantileMethod type = default(QuantileMethod), bool inPlace = false)

Parameters

Type	Name	Description
System.Int32[]	values	An integer array containing the vector members.
System.Boolean	alreadySorted	A boolean parameter informing if the given values have already been sorted.
QuantileMethod	type	The quartile definition that should be used. See QuantileMethod for datails.
System.Boolean	inPlace	Pass true if the method is allowed to sort `values` in place, overwriting the its original order.

Returns

Type	Description
System.Double	The median of the given data.

View Source

Mode<T>(T[])

Computes the Mode of the given values.

Declaration

public static T Mode<T>(this T[] values)

Parameters

Type	Name	Description
T[]	values	A number array containing the vector values.

Returns

Type	Description
T	The most common value in the given data.

Type Parameters

Name	Description
T

View Source

Mode<T>(T[], Boolean, Boolean)

Computes the Mode of the given values.

Declaration

public static T Mode<T>(this T[] values, bool inPlace, bool alreadySorted = false)

Parameters

Type	Name	Description
T[]	values	A number array containing the vector values.
System.Boolean	inPlace	True to perform the operation in place, altering the original input vector.
System.Boolean	alreadySorted	Pass true if the list of values is already sorted.

Returns

Type	Description
T	The most common value in the given data.

Type Parameters

Name	Description
T

View Source

Mode<T>(T[], out Int32)

Computes the Mode of the given values.

Declaration

public static T Mode<T>(this T[] values, out int count)

Parameters

Type	Name	Description
T[]	values	A number array containing the vector values.
System.Int32	count	Returns how many times the detected mode happens in the values.

Returns

Type	Description
T	The most common value in the given data.

Type Parameters

Name	Description
T

View Source

Mode<T>(T[], out Int32, Boolean, Boolean)

Computes the Mode of the given values.

Declaration

public static T Mode<T>(this T[] values, out int count, bool inPlace, bool alreadySorted = false)

Parameters

Type	Name	Description
T[]	values	A number array containing the vector values.
System.Int32	count	Returns how many times the detected mode happens in the values.
System.Boolean	inPlace	True to perform the operation in place, altering the original input vector.
System.Boolean	alreadySorted	Pass true if the list of values is already sorted.

Returns

Type	Description
T	The most common value in the given data.

Type Parameters

Name	Description
T

View Source

Mode<T>(T[][])

Calculates the matrix Modes vector.

Declaration

public static T[] Mode<T>(this T[][] matrix)

Parameters

Type	Name	Description
T[][]	matrix	A matrix whose modes will be calculated.

Returns

Type	Description
T[]	Returns a vector containing the modes of the given matrix.

Type Parameters

Name	Description
T

View Source

Mode<T>(T[,])

Calculates the matrix Modes vector.

Declaration

public static T[] Mode<T>(this T[, ] matrix)

Parameters

Type	Name	Description
T[,]	matrix	A matrix whose modes will be calculated.

Returns

Type	Description
T[]	Returns a vector containing the modes of the given matrix.

Type Parameters

Name	Description
T

View Source

PooledCovariance(Double[,][], Double[])

Calculates the weighted pooled covariance matrix from a set of covariance matrices.

Declaration

public static double[, ] PooledCovariance(double[, ][] covariances, double[] weights)

Parameters

Type	Name	Description
System.Double[,][]	covariances
System.Double[]	weights

Returns

Type	Description
System.Double[,]

View Source

PooledStandardDeviation(Boolean, Double[][])

Computes the pooled standard deviation of the given values.

Declaration

public static double PooledStandardDeviation(bool unbiased, params double[][] samples)

Parameters

Type	Name	Description
System.Boolean	unbiased	True to compute a pooled standard deviation using unbiased estimates of the population variance; false otherwise. Default is true.
System.Double[][]	samples	The grouped samples.

Returns

Type	Description
System.Double

View Source

PooledStandardDeviation(Double[][])

Computes the pooled standard deviation of the given values.

Declaration

public static double PooledStandardDeviation(params double[][] samples)

Parameters

Type	Name	Description
System.Double[][]	samples	The grouped samples.

Returns

Type	Description
System.Double

View Source

PooledStandardDeviation(Int32[], Double[], Boolean)

Computes the pooled standard deviation of the given values.

Declaration

public static double PooledStandardDeviation(int[] sizes, double[] variances, bool unbiased = true)

Parameters

Type	Name	Description
System.Int32[]	sizes	The number of samples used to compute the `variances`.
System.Double[]	variances	The unbiased variances for the samples.
System.Boolean	unbiased	True to compute a pooled standard deviation using unbiased estimates of the population variance; false otherwise. Default is true.

Returns

Type	Description
System.Double

View Source

PooledVariance(Boolean, Double[][])

Computes the pooled variance of the given values.

Declaration

public static double PooledVariance(bool unbiased, params double[][] samples)

Parameters

Type	Name	Description
System.Boolean	unbiased	True to obtain an unbiased estimate of the population variance; false otherwise. Default is true.
System.Double[][]	samples	The grouped samples.

Returns

Type	Description
System.Double

View Source

PooledVariance(Double[][])

Computes the pooled variance of the given values.

Declaration

public static double PooledVariance(params double[][] samples)

Parameters

Type	Name	Description
System.Double[][]	samples	The grouped samples.

Returns

Type	Description
System.Double

View Source

PooledVariance(Int32[], Double[], Boolean)

Computes the pooled variance of the given values.

Declaration

public static double PooledVariance(int[] sizes, double[] variances, bool unbiased = true)

Parameters

Type	Name	Description
System.Int32[]	sizes	The number of samples used to compute the `variances`.
System.Double[]	variances	The unbiased variances for the samples.
System.Boolean	unbiased	True to obtain an unbiased estimate of the population variance; false otherwise. Default is true.

Returns

Type	Description
System.Double

View Source

Quantile(Double[], Double, Boolean, QuantileMethod, Boolean)

Computes single quantile for the given sequence.

Declaration

public static double Quantile(this double[] values, double probabilities, bool alreadySorted = false, QuantileMethod type = default(QuantileMethod), bool inPlace = false)

Parameters

Type	Name	Description
System.Double[]	values	The sequence of observations.
System.Double	probabilities	The auantile probability.
System.Boolean	alreadySorted	A boolean parameter informing if the given values have already been sorted.
QuantileMethod	type	The quantile type, 1...9.
System.Boolean	inPlace	Pass true if the method is allowed to sort `values` in place, overwriting the its original order.

Returns

Type	Description
System.Double	Quantile value.

View Source

Quantiles(Double[], Double[], Boolean, QuantileMethod, Boolean)

Computes multiple quantiles for the given sequence.

Declaration

public static double[] Quantiles(this double[] values, double[] probabilities, bool alreadySorted = false, QuantileMethod type = default(QuantileMethod), bool inPlace = false)

Parameters

Type	Name	Description
System.Double[]	values	The sequence of observations.
System.Double[]	probabilities	The sequence of quantile probabilities.
System.Boolean	alreadySorted	A boolean parameter informing if the given values have already been sorted.
QuantileMethod	type	The quantile type, 1...9.
System.Boolean	inPlace	Pass true if the method is allowed to sort `values` in place, overwriting the its original order.

Returns

Type	Description
System.Double[]	Quantile value.

View Source

Quartiles(Double[], out NumericRange, Boolean, QuantileMethod, Boolean)

Computes the Quartiles of the given values.

Declaration

public static double Quartiles(this double[] values, out NumericRange range, bool alreadySorted = false, QuantileMethod type = default(QuantileMethod), bool inPlace = false)

Parameters

Type	Name	Description
System.Double[]	values	An integer array containing the vector members.
NumericRange	range	The inter-quartile range for the values.
System.Boolean	alreadySorted	A boolean parameter informing if the given values have already been sorted.
QuantileMethod	type	The quartile definition that should be used. See QuantileMethod for datails.
System.Boolean	inPlace	Pass true if the method is allowed to sort `values` in place, overwriting the its original order.

Returns

Type	Description
System.Double	The second quartile, the median of the given data.

View Source

Quartiles(Double[], out Double, out Double, Boolean, QuantileMethod, Boolean)

Computes the Quartiles of the given values.

Declaration

public static double Quartiles(this double[] values, out double q1, out double q3, bool alreadySorted = false, QuantileMethod type = default(QuantileMethod), bool inPlace = false)

Parameters

Type	Name	Description
System.Double[]	values	An integer array containing the vector members.
System.Double	q1	The first quartile.
System.Double	q3	The third quartile.
System.Boolean	alreadySorted	A boolean parameter informing if the given values have already been sorted.
QuantileMethod	type	The quartile definition that should be used. See QuantileMethod for datails.
System.Boolean	inPlace	Pass true if the method is allowed to sort `values` in place, overwriting the its original order.

Returns

Type	Description
System.Double	The second quartile, the median of the given data.

View Source

Quartiles(Double[][], out NumericRange[], QuantileMethod)

Computes the Quartiles of the given values.

Declaration

public static double[] Quartiles(this double[][] matrix, out NumericRange[] range, QuantileMethod type = default(QuantileMethod))

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose medians and quartiles will be calculated.
NumericRange[]	range	The inter-quartile range for the values.
QuantileMethod	type	The quartile definition that should be used. See QuantileMethod for datails.

Returns

Type	Description
System.Double[]	The second quartile, the median of the given data.

View Source

Quartiles(Double[][], out Double[], out Double[], QuantileMethod)

Computes the Quartiles of the given values.

Declaration

public static double[] Quartiles(double[][] matrix, out double[] q1, out double[] q3, QuantileMethod type = default(QuantileMethod))

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose medians and quartiles will be calculated.
System.Double[]	q1	The first quartile for each column.
System.Double[]	q3	The third quartile for each column.
QuantileMethod	type	The quartile definition that should be used. See QuantileMethod for datails.

Returns

Type	Description
System.Double[]	The second quartile, the median of the given data.

View Source

Quartiles(Double[,], out NumericRange[], QuantileMethod)

Computes the Quartiles of the given values.

Declaration

public static double[] Quartiles(this double[, ] matrix, out NumericRange[] range, QuantileMethod type = default(QuantileMethod))

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose medians and quartiles will be calculated.
NumericRange[]	range	The inter-quartile range for the values.
QuantileMethod	type	The quartile definition that should be used. See QuantileMethod for datails.

Returns

Type	Description
System.Double[]	The second quartile, the median of the given data.

View Source

Quartiles(Double[,], out Double[], out Double[], QuantileMethod)

Computes the Quartiles of the given values.

Declaration

public static double[] Quartiles(double[, ] matrix, out double[] q1, out double[] q3, QuantileMethod type = default(QuantileMethod))

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose medians and quartiles will be calculated.
System.Double[]	q1	The first quartile for each column.
System.Double[]	q3	The third quartile for each column.
QuantileMethod	type	The quartile definition that should be used. See QuantileMethod for datails.

Returns

Type	Description
System.Double[]	The second quartile, the median of the given data.

View Source

Scatter(Double[][], Double, Int32)

Calculates the scatter matrix of a sample matrix.

Declaration

public static double[][] Scatter(this double[][] matrix, double divisor, int dimension = 0)

Parameters

Type	Name	Description
System.Double[][]	matrix	A number multi-dimensional array containing the matrix values.
System.Double	divisor	A real number to divide each member of the matrix.
System.Int32	dimension	Pass 0 to if mean vector is a row vector, 1 otherwise. Default value is 0.

Returns

Type	Description
System.Double[][]	The covariance matrix.

Remarks

By dividing the Scatter matrix by the sample size, we get the population Covariance matrix. By dividing by the sample size minus one, we get the sample Covariance matrix.

View Source

Scatter(Double[][], Double[])

Calculates the scatter matrix of a sample matrix.

Declaration

public static double[][] Scatter(this double[][] matrix, double[] means)

Parameters

Type	Name	Description
System.Double[][]	matrix	A number multi-dimensional array containing the matrix values.
System.Double[]	means	The mean value of the given values, if already known.

Returns

Type	Description
System.Double[][]	The covariance matrix.

Remarks

By dividing the Scatter matrix by the sample size, we get the population Covariance matrix. By dividing by the sample size minus one, we get the sample Covariance matrix.

View Source

Scatter(Double[][], Double[], Double)

Calculates the scatter matrix of a sample matrix.

Declaration

public static double[][] Scatter(this double[][] matrix, double[] means, double divisor)

Parameters

Type	Name	Description
System.Double[][]	matrix	A number multi-dimensional array containing the matrix values.
System.Double[]	means	The mean value of the given values, if already known.
System.Double	divisor	A real number to divide each member of the matrix.

Returns

Type	Description
System.Double[][]	The covariance matrix.

Remarks

By dividing the Scatter matrix by the sample size, we get the population Covariance matrix. By dividing by the sample size minus one, we get the sample Covariance matrix.

View Source

Scatter(Double[][], Double[], Double, Int32)

Calculates the scatter matrix of a sample matrix.

Declaration

public static double[][] Scatter(double[][] matrix, double[] means, double divisor, int dimension)

Parameters

Type	Name	Description
System.Double[][]	matrix	A number multi-dimensional array containing the matrix values.
System.Double[]	means	The mean value of the given values, if already known.
System.Double	divisor	A real number to divide each member of the matrix.
System.Int32	dimension	Pass 0 to if mean vector is a row vector, 1 otherwise. Default value is 0.

Returns

Type	Description
System.Double[][]	The covariance matrix.

Remarks

By dividing the Scatter matrix by the sample size, we get the population Covariance matrix. By dividing by the sample size minus one, we get the sample Covariance matrix.

View Source

Scatter(Double[][], Double[], Int32)

Calculates the scatter matrix of a sample matrix.

Declaration

public static double[][] Scatter(this double[][] matrix, double[] means, int dimension)

Parameters

Type	Name	Description
System.Double[][]	matrix	A number multi-dimensional array containing the matrix values.
System.Double[]	means	The mean value of the given values, if already known.
System.Int32	dimension	Pass 0 to if mean vector is a row vector, 1 otherwise. Default value is 0.

Returns

Type	Description
System.Double[][]	The covariance matrix.

Remarks

By dividing the Scatter matrix by the sample size, we get the population Covariance matrix. By dividing by the sample size minus one, we get the sample Covariance matrix.

View Source

Scatter(Double[,], Double[])

Calculates the scatter matrix of a sample matrix.

Declaration

public static double[, ] Scatter(this double[, ] matrix, double[] means)

Parameters

Type	Name	Description
System.Double[,]	matrix	A number multi-dimensional array containing the matrix values.
System.Double[]	means	The mean value of the given values, if already known.

Returns

Type	Description
System.Double[,]	The covariance matrix.

Remarks

By dividing the Scatter matrix by the sample size, we get the population Covariance matrix. By dividing by the sample size minus one, we get the sample Covariance matrix.

View Source

Scatter(Double[,], Double[], Double)

Calculates the scatter matrix of a sample matrix.

Declaration

public static double[, ] Scatter(this double[, ] matrix, double[] means, double divisor)

Parameters

Type	Name	Description
System.Double[,]	matrix	A number multi-dimensional array containing the matrix values.
System.Double[]	means	The mean value of the given values, if already known.
System.Double	divisor	A real number to divide each member of the matrix.

Returns

Type	Description
System.Double[,]	The covariance matrix.

Remarks

By dividing the Scatter matrix by the sample size, we get the population Covariance matrix. By dividing by the sample size minus one, we get the sample Covariance matrix.

View Source

Scatter(Double[,], Double[], Double, Int32)

Calculates the scatter matrix of a sample matrix.

Declaration

public static double[, ] Scatter(this double[, ] matrix, double[] means, double divisor, int dimension)

Parameters

Type	Name	Description
System.Double[,]	matrix	A number multi-dimensional array containing the matrix values.
System.Double[]	means	The mean value of the given values, if already known.
System.Double	divisor	A real number to divide each member of the matrix.
System.Int32	dimension	Pass 0 if the mean vector is a row vector, 1 otherwise. Default value is 0.

Returns

Type	Description
System.Double[,]	The covariance matrix.

Remarks

By dividing the Scatter matrix by the sample size, we get the population Covariance matrix. By dividing by the sample size minus one, we get the sample Covariance matrix.

View Source

Scatter(Double[,], Double[], Int32)

Calculates the scatter matrix of a sample matrix.

Declaration

public static double[, ] Scatter(this double[, ] matrix, double[] means, int dimension)

Parameters

Type	Name	Description
System.Double[,]	matrix	A number multi-dimensional array containing the matrix values.
System.Double[]	means	The mean value of the given values, if already known.
System.Int32	dimension	Pass 0 to if mean vector is a row vector, 1 otherwise. Default value is 0.

Returns

Type	Description
System.Double[,]	The covariance matrix.

Remarks

By dividing the Scatter matrix by the sample size, we get the population Covariance matrix. By dividing by the sample size minus one, we get the sample Covariance matrix.

View Source

Skewness(Double[], Boolean)

Computes the Skewness for the given values.

Declaration

public static double Skewness(this double[] values, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector values.
System.Boolean	unbiased	True to compute the unbiased estimate of the population skewness, false otherwise. Default is true (compute the unbiased estimator).

Returns

Type	Description
System.Double	The skewness of the given data.

Remarks

Skewness characterizes the degree of asymmetry of a distribution around its mean. Positive skewness indicates a distribution with an asymmetric tail extending towards more positive values. Negative skewness indicates a distribution with an asymmetric tail extending towards more negative values.

View Source

Skewness(Double[], Double, Boolean)

Computes the Skewness for the given values.

Declaration

public static double Skewness(this double[] values, double mean, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector values.
System.Double	mean	The values' mean, if already known.
System.Boolean	unbiased	True to compute the unbiased estimate of the population skewness, false otherwise. Default is true (compute the unbiased estimator).

Returns

Type	Description
System.Double	The skewness of the given data.

Remarks

View Source

Skewness(Double[][], Boolean)

Computes the Skewness for the given values.

Declaration

public static double[] Skewness(this double[][] matrix, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[][]	matrix	A number matrix containing the matrix values.
System.Boolean	unbiased	True to compute the unbiased estimate of the population skewness, false otherwise. Default is true (compute the unbiased estimator).

Returns

Type	Description
System.Double[]	The skewness of the given data.

Remarks

View Source

Skewness(Double[][], Double[], Boolean)

Computes the Skewness vector for the given matrix.

Declaration

public static double[] Skewness(this double[][] matrix, double[] means, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[][]	matrix	A number array containing the vector values.
System.Double[]	means	The column means, if known.
System.Boolean	unbiased	True to compute the unbiased estimate of the population skewness, false otherwise. Default is true (compute the unbiased estimator).

Returns

Type	Description
System.Double[]	The skewness of the given data.

Remarks

View Source

Skewness(Double[,], Boolean)

Computes the Skewness for the given values.

Declaration

public static double[] Skewness(this double[, ] matrix, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[,]	matrix	A number matrix containing the matrix values.
System.Boolean	unbiased	True to compute the unbiased estimate of the population skewness, false otherwise. Default is true (compute the unbiased estimator).

Returns

Type	Description
System.Double[]	The skewness of the given data.

Remarks

View Source

Skewness(Double[,], Double[], Boolean)

Computes the Skewness vector for the given matrix.

Declaration

public static double[] Skewness(this double[, ] matrix, double[] means, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[,]	matrix	A number array containing the vector values.
System.Double[]	means	The mean value for the given values, if already known.
System.Boolean	unbiased	True to compute the unbiased estimate of the population skewness, false otherwise. Default is true (compute the unbiased estimator).

Returns

Type	Description
System.Double[]	The skewness of the given data.

Remarks

View Source

StandardDeviation(Double[], Boolean)

Computes the Standard Deviation of the given values.

Declaration

public static double StandardDeviation(this double[] values, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[]	values	A double array containing the vector members.
System.Boolean	unbiased	Pass true to compute the standard deviation using the sample variance. Pass false to compute it using the population variance. See remarks for more details.

Returns

Type	Description
System.Double	The standard deviation of the given data.

Remarks

Setting unbiased to true will make this method compute the standard deviation σ using the sample variance, which is an unbiased estimator of the true population variance. Setting this parameter to true will thus compute σ using the following formula:

                      N
   σ² = 1 / (N - 1)  ∑   (x_i − μ)²
                      i=1

Setting unbiased to false will assume the given values already represent the whole population, and will compute the population variance using the formula:

                      N
   σ² =   (1 / N)    ∑   (x_i − μ)²
                      i=1

View Source

StandardDeviation(Double[], Double, Boolean)

Computes the Standard Deviation of the given values.

Declaration

public static double StandardDeviation(this double[] values, double mean, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[]	values	A double array containing the vector members.
System.Double	mean	The mean of the vector, if already known.
System.Boolean	unbiased	Pass true to compute the standard deviation using the sample variance. Pass false to compute it using the population variance. See remarks for more details.

Returns

Type	Description
System.Double	The standard deviation of the given data.

Remarks

                      N
   σ² = 1 / (N - 1)  ∑   (x_i − μ)²
                      i=1

Setting unbiased to false will assume the given values already represent the whole population, and will compute the population variance using the formula:

                      N
   σ² =   (1 / N)    ∑   (x_i − μ)²
                      i=1

View Source

StandardDeviation(Double[][], Boolean)

Calculates the matrix Standard Deviations vector.

Declaration

public static double[] StandardDeviation(this double[][] matrix, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose deviations will be calculated.
System.Boolean	unbiased	Pass true to compute the standard deviation using the sample variance. Pass false to compute it using the population variance. See remarks for more details.

Returns

Type	Description
System.Double[]	Returns a vector containing the standard deviations of the given matrix.

Remarks

                      N
   σ² = 1 / (N - 1)  ∑   (x_i − μ)²
                      i=1

Setting unbiased to false will assume the given values already represent the whole population, and will compute the population variance using the formula:

                      N
   σ² =   (1 / N)    ∑   (x_i − μ)²
                      i=1

View Source

StandardDeviation(Double[][], Double[], Boolean)

Calculates the matrix Standard Deviations vector.

Declaration

public static double[] StandardDeviation(this double[][] matrix, double[] means, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose deviations will be calculated.
System.Double[]	means	The mean vector containing already calculated means for each column of the matrix.
System.Boolean	unbiased	Pass true to compute the standard deviation using the sample variance. Pass false to compute it using the population variance. See remarks for more details.

Returns

Type	Description
System.Double[]	Returns a vector containing the standard deviations of the given matrix.

Remarks

                      N
   σ² = 1 / (N - 1)  ∑   (x_i − μ)²
                      i=1

Setting unbiased to false will assume the given values already represent the whole population, and will compute the population variance using the formula:

                      N
   σ² =   (1 / N)    ∑   (x_i − μ)²
                      i=1

View Source

StandardDeviation(Double[,])

Calculates the matrix Standard Deviations vector.

Declaration

public static double[] StandardDeviation(this double[, ] matrix)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose deviations will be calculated.

Returns

Type	Description
System.Double[]	Returns a vector containing the standard deviations of the given matrix.

View Source

StandardDeviation(Double[,], Double[])

Calculates the matrix Standard Deviations vector.

Declaration

public static double[] StandardDeviation(this double[, ] matrix, double[] means)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose deviations will be calculated.
System.Double[]	means	The mean vector containing already calculated means for each column of the matrix.

Returns

Type	Description
System.Double[]	Returns a vector containing the standard deviations of the given matrix.

View Source

StandardDeviation(Int32[], Double)

Computes the Standard Deviation of the given values.

Declaration

public static double StandardDeviation(this int[] values, double mean)

Parameters

Type	Name	Description
System.Int32[]	values	An integer array containing the vector members.
System.Double	mean	The mean of the vector, if already known.

Returns

Type	Description
System.Double	The standard deviation of the given data.

View Source

StandardDeviation(Single[])

Computes the Standard Deviation of the given values.

Declaration

public static double StandardDeviation(this float[] values)

Parameters

Type	Name	Description
System.Single[]	values	A double array containing the vector members.

Returns

Type	Description
System.Double	The standard deviation of the given data.

View Source

StandardDeviation(Single[], Single)

Computes the Standard Deviation of the given values.

Declaration

public static float StandardDeviation(this float[] values, float mean)

Parameters

Type	Name	Description
System.Single[]	values	A float array containing the vector members.
System.Single	mean	The mean of the vector, if already known.

Returns

Type	Description
System.Single	The standard deviation of the given data.

View Source

StandardError(Double[])

Computes the Standard Error for a sample size, which estimates the standard deviation of the sample mean based on the population mean.

Declaration

public static double StandardError(double[] values)

Parameters

Type	Name	Description
System.Double[]	values	A double array containing the samples.

Returns

Type	Description
System.Double	The standard error for the sample.

View Source

StandardError(Double[,])

Computes the Standard Error vector for a given matrix.

Declaration

public static double[] StandardError(double[, ] matrix)

Parameters

Type	Name	Description
System.Double[,]	matrix	A number multi-dimensional array containing the matrix values.

Returns

Type	Description
System.Double[]	Returns the standard error vector for the matrix.

View Source

StandardError(Int32, Double)

Computes the Standard Error for a sample size, which estimates the standard deviation of the sample mean based on the population mean.

Declaration

public static double StandardError(int samples, double standardDeviation)

Parameters

Type	Name	Description
System.Int32	samples	The sample size.
System.Double	standardDeviation	The sample standard deviation.

Returns

Type	Description
System.Double	The standard error for the sample.

View Source

StandardError(Int32, Double[])

Computes the Standard Error vector for a given matrix.

Declaration

public static double[] StandardError(int samples, double[] standardDeviations)

Parameters

Type	Name	Description
System.Int32	samples	The number of samples in the matrix.
System.Double[]	standardDeviations	The values' standard deviation vector, if already known.

Returns

Type	Description
System.Double[]	Returns the standard error vector for the matrix.

View Source

TruncatedMean(Double[], Double, Boolean, Boolean)

Computes the truncated (trimmed) mean of the given values.

Declaration

public static double TruncatedMean(this double[] values, double percent, bool inPlace = false, bool alreadySorted = false)

Parameters

Type	Name	Description
System.Double[]	values	A double array containing the vector members.
System.Double	percent	The percentage of observations to drop from the sample.
System.Boolean	inPlace	Whether to perform operations in place, overwriting the original vector.
System.Boolean	alreadySorted	A boolean parameter informing if the given values have already been sorted.

Returns

Type	Description
System.Double	The mean of the given data.

View Source

UpperQuartile(Double[], Boolean, QuantileMethod, Boolean)

Computes the upper quartile (Q3) for the given data.

Declaration

public static double UpperQuartile(this double[] values, bool alreadySorted = false, QuantileMethod type = default(QuantileMethod), bool inPlace = false)

Parameters

Type	Name	Description
System.Double[]	values	An integer array containing the vector members.
System.Boolean	alreadySorted	A boolean parameter informing if the given values have already been sorted.
QuantileMethod	type	The quartile definition that should be used. See QuantileMethod for datails.
System.Boolean	inPlace	Pass true if the method is allowed to sort `values` in place, overwriting the its original order.

Returns

Type	Description
System.Double	The third quartile of the given data.

View Source

Variance(Double[])

Computes the Variance of the given values.

Declaration

public static double Variance(this double[] values)

Parameters

Type	Name	Description
System.Double[]	values	A double precision number array containing the vector members.

Returns

Type	Description
System.Double	The variance of the given data.

View Source

Variance(Double[], Boolean)

Computes the Variance of the given values.

Declaration

public static double Variance(this double[] values, bool unbiased)

Parameters

Type	Name	Description
System.Double[]	values	A double precision number array containing the vector members.
System.Boolean	unbiased	Pass true to compute the sample variance; or pass false to compute the population variance. See remarks for more details.

Returns

Type	Description
System.Double	The variance of the given data.

Remarks

                      N
   σ² = 1 / (N - 1)  ∑   (x_i − μ)²
                      i=1

Setting unbiased to false will assume the given values already represent the whole population, and will compute the population variance using the formula:

                      N
   σ² =   (1 / N)    ∑   (x_i − μ)²
                      i=1

View Source

Variance(Double[], Double)

Computes the Variance of the given values.

Declaration

public static double Variance(this double[] values, double mean)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector members.
System.Double	mean	The mean of the array, if already known.

Returns

Type	Description
System.Double	The variance of the given data.

View Source

Variance(Double[], Double, Boolean)

Computes the Variance of the given values.

Declaration

public static double Variance(this double[] values, double mean, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector members.
System.Double	mean	The mean of the array, if already known.
System.Boolean	unbiased	Pass true to compute the sample variance; or pass false to compute the population variance. See remarks for more details.

Returns

Type	Description
System.Double	The variance of the given data.

Remarks

                      N
   σ² = 1 / (N - 1)  ∑   (x_i − μ)²
                      i=1

Setting unbiased to false will assume the given values already represent the whole population, and will compute the population variance using the formula:

                      N
   σ² =   (1 / N)    ∑   (x_i − μ)²
                      i=1

View Source

Variance(Double[][])

Calculates the matrix Variance vector.

Declaration

public static double[] Variance(this double[][] matrix)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose variances will be calculated.

Returns

Type	Description
System.Double[]	Returns a vector containing the variances of the given matrix.

View Source

Variance(Double[][], Double[], Boolean)

Calculates the matrix Variance vector.

Declaration

public static double[] Variance(this double[][] matrix, double[] means, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose variances will be calculated.
System.Double[]	means	The mean vector containing already calculated means for each column of the matrix.
System.Boolean	unbiased	Pass true to compute the sample variance; or pass false to compute the population variance. See remarks for more details.

Returns

Type	Description
System.Double[]	Returns a vector containing the variances of the given matrix.

Remarks

                      N
   σ² = 1 / (N - 1)  ∑   (x_i − μ)²
                      i=1

Setting unbiased to false will assume the given values already represent the whole population, and will compute the population variance using the formula:

                      N
   σ² =   (1 / N)    ∑   (x_i − μ)²
                      i=1

View Source

Variance(Double[,])

Calculates the matrix Variance vector.

Declaration

public static double[] Variance(this double[, ] matrix)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose variances will be calculated.

Returns

Type	Description
System.Double[]	Returns a vector containing the variances of the given matrix.

View Source

Variance(Double[,], Double[])

Calculates the matrix Variance vector.

Declaration

public static double[] Variance(this double[, ] matrix, double[] means)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose variances will be calculated.
System.Double[]	means	The mean vector containing already calculated means for each column of the matrix.

Returns

Type	Description
System.Double[]	Returns a vector containing the variances of the given matrix.

View Source

Variance(Int32[])

Computes the Variance of the given values.

Declaration

public static double Variance(this int[] values)

Parameters

Type	Name	Description
System.Int32[]	values	An integer number array containing the vector members.

Returns

Type	Description
System.Double	The variance of the given data.

View Source

Variance(Int32[], Boolean)

Computes the Variance of the given values.

Declaration

public static double Variance(this int[] values, bool unbiased)

Parameters

Type	Name	Description
System.Int32[]	values	An integer number array containing the vector members.
System.Boolean	unbiased	Pass true to compute the sample variance; or pass false to compute the population variance. See remarks for more details.

Returns

Type	Description
System.Double	The variance of the given data.

Remarks

                      N
   σ² = 1 / (N - 1)  ∑   (x_i − μ)²
                      i=1

Setting unbiased to false will assume the given values already represent the whole population, and will compute the population variance using the formula:

                      N
   σ² =   (1 / N)    ∑   (x_i − μ)²
                      i=1

View Source

Variance(Int32[], Double, Boolean)

Computes the Variance of the given values.

Declaration

public static double Variance(this int[] values, double mean, bool unbiased = true)

Parameters

Type	Name	Description
System.Int32[]	values	A number array containing the vector members.
System.Double	mean	The mean of the array, if already known.
System.Boolean	unbiased	Pass true to compute the sample variance; or pass false to compute the population variance. See remarks for more details.

Returns

Type	Description
System.Double	The variance of the given data.

Remarks

                      N
   σ² = 1 / (N - 1)  ∑   (x_i − μ)²
                      i=1

Setting unbiased to false will assume the given values already represent the whole population, and will compute the population variance using the formula:

                      N
   σ² =   (1 / N)    ∑   (x_i − μ)²
                      i=1

View Source

Variance(Single[])

Computes the Variance of the given values.

Declaration

public static double Variance(this float[] values)

Parameters

Type	Name	Description
System.Single[]	values	A single precision number array containing the vector members.

Returns

Type	Description
System.Double	The variance of the given data.

View Source

Variance(Single[], Single)

Computes the Variance of the given values.

Declaration

public static float Variance(this float[] values, float mean)

Parameters

Type	Name	Description
System.Single[]	values	A number array containing the vector members.
System.Single	mean	The mean of the array, if already known.

Returns

Type	Description
System.Single	The variance of the given data.

View Source

WeightedCovariance(Double[][], Double[], Double[])

Calculates the covariance matrix of a sample matrix.

Declaration

public static double[, ] WeightedCovariance(this double[][] matrix, double[] weights, double[] means)

Parameters

Type	Name	Description
System.Double[][]	matrix	A number multi-dimensional array containing the matrix values.
System.Double[]	weights	An unit vector containing the importance of each sample in . The sum of this array elements should add up to 1.
System.Double[]	means	The mean value of the given values, if already known.

Returns

Type	Description
System.Double[,]	The covariance matrix.

View Source

WeightedCovariance(Double[][], Double[], Double[], Int32)

Calculates the covariance matrix of a sample matrix.

Declaration

public static double[, ] WeightedCovariance(this double[][] matrix, double[] weights, double[] means, int dimension)

Parameters

Type	Name	Description
System.Double[][]	matrix	A number multi-dimensional array containing the matrix values.
System.Double[]	weights	An unit vector containing the importance of each sample in . The sum of this array elements should add up to 1.
System.Double[]	means	The mean value of the given values, if already known.
System.Int32	dimension	Pass 0 to if mean vector is a row vector, 1 otherwise. Default value is 0.

Returns

Type	Description
System.Double[,]	The covariance matrix.

View Source

WeightedCovariance(Double[][], Double[], Int32)

Calculates the covariance matrix of a sample matrix.

Declaration

public static double[, ] WeightedCovariance(this double[][] matrix, double[] weights, int dimension = 0)

Parameters

Type	Name	Description
System.Double[][]	matrix	A number multi-dimensional array containing the matrix values.
System.Double[]	weights	An unit vector containing the importance of each sample in . The sum of this array elements should add up to 1.
System.Int32	dimension	Pass 0 to if mean vector is a row vector, 1 otherwise. Default value is 0.

Returns

Type	Description
System.Double[,]	The covariance matrix.

View Source

WeightedCovariance(Double[][], Int32[], Double[], Int32)

Calculates the covariance matrix of a sample matrix.

Declaration

public static double[, ] WeightedCovariance(this double[][] matrix, int[] weights, double[] means, int dimension)

Parameters

Type	Name	Description
System.Double[][]	matrix	A number multi-dimensional array containing the matrix values.
System.Int32[]	weights	The number of times each sample should be repeated.
System.Double[]	means	The mean value of the given values, if already known.
System.Int32	dimension	Pass 0 to if mean vector is a row vector, 1 otherwise. Default value is 0.

Returns

Type	Description
System.Double[,]	The covariance matrix.

View Source

WeightedCovariance(Double[][], Int32[], Int32)

Calculates the covariance matrix of a sample matrix.

Declaration

public static double[, ] WeightedCovariance(this double[][] matrix, int[] weights, int dimension = 0)

Parameters

Type	Name	Description
System.Double[][]	matrix	A number multi-dimensional array containing the matrix values.
System.Int32[]	weights	The number of times each sample should be repeated.
System.Int32	dimension	Pass 0 to if mean vector is a row vector, 1 otherwise. Default value is 0.

Returns

Type	Description
System.Double[,]	The covariance matrix.

View Source

WeightedEntropy(IList<Int32>, IList<Double>, Int32)

Computes the entropy for the given values.

Declaration

public static double WeightedEntropy(IList<int> values, IList<double> weights, int classes)

Parameters

Type	Name	Description
IList<System.Int32>	values	An array of integer symbols.
IList<System.Double>	weights	The importance for each sample.
System.Int32	classes	The number of distinct classes.

Returns

Type	Description
System.Double	The evaluated entropy.

View Source

WeightedEntropy(IList<Int32>, IList<Double>, Int32, Int32)

Computes the entropy for the given values.

Declaration

public static double WeightedEntropy(IList<int> values, IList<double> weights, int startValue, int endValue)

Parameters

Type	Name	Description
IList<System.Int32>	values	An array of integer symbols.
IList<System.Double>	weights	The importance for each sample.
System.Int32	startValue	The starting symbol.
System.Int32	endValue	The ending symbol.

Returns

Type	Description
System.Double	The evaluated entropy.

View Source

WeightedEntropy(Double[], Double[], Func<Double, Double>)

Computes the entropy function for a set of numerical values in a given Probability Density Function (pdf).

Declaration

public static double WeightedEntropy(this double[] values, double[] weights, Func<double, double> pdf)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector values.
System.Double[]	weights	The importance for each sample.
Func<System.Double, System.Double>	pdf	A probability distribution function.

Returns

Type	Description
System.Double	The distribution's entropy for the given values.

View Source

WeightedEntropy(Double[], Double[], Double, Double)

Computes the entropy for the given values.

Declaration

public static double WeightedEntropy(double[] values, double[] weights, double startValue, double endValue)

Parameters

Type	Name	Description
System.Double[]	values	An array of integer symbols.
System.Double[]	weights	The importance for each sample.
System.Double	startValue	The starting symbol.
System.Double	endValue	The ending symbol.

Returns

Type	Description
System.Double	The evaluated entropy.

View Source

WeightedEntropy(Double[], Double[], Int32)

Computes the entropy for the given values.

Declaration

public static double WeightedEntropy(double[] values, double[] weights, int classes)

Parameters

Type	Name	Description
System.Double[]	values	An array of integer symbols.
System.Double[]	weights	The importance for each sample.
System.Int32	classes	The number of distinct classes.

Returns

Type	Description
System.Double	The evaluated entropy.

View Source

WeightedEntropy(Double[], Double[], Int32, Int32)

Computes the entropy for the given values.

Declaration

public static double WeightedEntropy(double[] values, double[] weights, int startValue, int endValue)

Parameters

Type	Name	Description
System.Double[]	values	An array of integer symbols.
System.Double[]	weights	The importance for each sample.
System.Int32	startValue	The starting symbol.
System.Int32	endValue	The ending symbol.

Returns

Type	Description
System.Double	The evaluated entropy.

View Source

WeightedEntropy(Double[], Int32[], Func<Double, Double>)

Computes the entropy function for a set of numerical values in a given Probability Density Function (pdf).

Declaration

public static double WeightedEntropy(this double[] values, int[] weights, Func<double, double> pdf)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector values.
System.Int32[]	weights	The repetition counts for each sample.
Func<System.Double, System.Double>	pdf	A probability distribution function.

Returns

Type	Description
System.Double	The distribution's entropy for the given values.

View Source

WeightedEntropy(Int32[], Double[], Int32)

Computes the entropy for the given values.

Declaration

public static double WeightedEntropy(int[] values, double[] weights, int classes)

Parameters

Type	Name	Description
System.Int32[]	values	An array of integer symbols.
System.Double[]	weights	The importance for each sample.
System.Int32	classes	The number of distinct classes.

Returns

Type	Description
System.Double	The evaluated entropy.

View Source

WeightedMax(Double[], Double[], out Int32, Boolean)

Gets the maximum value in a vector of observations that has a weight higher than zero.

Declaration

public static double WeightedMax(this double[] values, double[] weights, out int imax, bool alreadySorted = false)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector values.
System.Double[]	weights	A vector containing the importance of each sample in .
System.Int32	imax	The index of the maximum element in the vector, or -1 if it could not be found.
System.Boolean	alreadySorted	Pass true if the list of values is already sorted.

Returns

Type	Description
System.Double	The maximum value in the given data.

View Source

WeightedMax(Double[], Int32[], out Int32, Boolean)

Gets the maximum value in a vector of observations that has a weight higher than zero.

Declaration

public static double WeightedMax(this double[] values, int[] weights, out int imax, bool alreadySorted = false)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector values.
System.Int32[]	weights	The number of times each sample should be repeated.
System.Int32	imax	The index of the maximum element in the vector, or -1 if it could not be found.
System.Boolean	alreadySorted	Pass true if the list of values is already sorted.

Returns

Type	Description
System.Double	The maximum value in the given data.

View Source

WeightedMean(Double[], Double[])

Computes the Weighted Mean of the given values.

Declaration

public static double WeightedMean(this double[] values, double[] weights)

Parameters

Type	Name	Description
System.Double[]	values	A double array containing the vector members.
System.Double[]	weights	An unit vector containing the importance of each sample in .

Returns

Type	Description
System.Double	The mean of the given data.

View Source

WeightedMean(Double[], Int32[])

Computes the Weighted Mean of the given values.

Declaration

public static double WeightedMean(this double[] values, int[] weights)

Parameters

Type	Name	Description
System.Double[]	values	A double array containing the vector members.
System.Int32[]	weights	A vector containing how many times each element in repeats itself in the non-weighted data.

Returns

Type	Description
System.Double	The mean of the given data.

View Source

WeightedMean(Double[][], Double[])

Calculates the weighted matrix Mean vector.

Declaration

public static double[] WeightedMean(this double[][] matrix, double[] weights)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose means will be calculated.
System.Double[]	weights	A vector containing the importance of each sample in the matrix.

Returns

Type	Description
System.Double[]	Returns a vector containing the means of the given matrix.

View Source

WeightedMean(Double[][], Double[], Int32)

Calculates the weighted matrix Mean vector.

Declaration

public static double[] WeightedMean(this double[][] matrix, double[] weights, int dimension = 0)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose means will be calculated.
System.Double[]	weights	A vector containing the importance of each sample in the matrix.
System.Int32	dimension	The dimension along which the means will be calculated. Pass 0 to compute a row vector containing the mean of each column, or 1 to compute a column vector containing the mean of each row. Default value is 0.

Returns

Type	Description
System.Double[]	Returns a vector containing the means of the given matrix.

View Source

WeightedMean(Double[][], Int32[])

Calculates the weighted matrix Mean vector.

Declaration

public static double[] WeightedMean(this double[][] matrix, int[] weights)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose means will be calculated.
System.Int32[]	weights	A vector containing the importance of each sample in the matrix.

Returns

Type	Description
System.Double[]	Returns a vector containing the means of the given matrix.

View Source

WeightedMean(Double[][], Int32[], Int32)

Calculates the weighted matrix Mean vector.

Declaration

public static double[] WeightedMean(this double[][] matrix, int[] weights, int dimension = 0)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose means will be calculated.
System.Int32[]	weights	A vector containing the importance of each sample in the matrix.
System.Int32	dimension	The dimension along which the means will be calculated. Pass 0 to compute a row vector containing the mean of each column, or 1 to compute a column vector containing the mean of each row. Default value is 0.

Returns

Type	Description
System.Double[]	Returns a vector containing the means of the given matrix.

View Source

WeightedMean(Double[,], Double[])

Calculates the weighted matrix Mean vector.

Declaration

public static double[] WeightedMean(this double[, ] matrix, double[] weights)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose means will be calculated.
System.Double[]	weights	A vector containing the importance of each sample in the matrix.

Returns

Type	Description
System.Double[]	Returns a vector containing the means of the given matrix.

View Source

WeightedMean(Double[,], Double[], Int32)

Calculates the weighted matrix Mean vector.

Declaration

public static double[] WeightedMean(this double[, ] matrix, double[] weights, int dimension = 0)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose means will be calculated.
System.Double[]	weights	A vector containing the importance of each sample in the matrix.
System.Int32	dimension	The dimension along which the means will be calculated. Pass 0 to compute a row vector containing the mean of each column, or 1 to compute a column vector containing the mean of each row. Default value is 0.

Returns

Type	Description
System.Double[]	Returns a vector containing the means of the given matrix.

View Source

WeightedMean(Double[,], Int32[])

Calculates the weighted matrix Mean vector.

Declaration

public static double[] WeightedMean(this double[, ] matrix, int[] weights)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose means will be calculated.
System.Int32[]	weights	A vector containing the importance of each sample in the matrix.

Returns

Type	Description
System.Double[]	Returns a vector containing the means of the given matrix.

View Source

WeightedMean(Double[,], Int32[], Int32)

Calculates the weighted matrix Mean vector.

Declaration

public static double[] WeightedMean(this double[, ] matrix, int[] weights, int dimension = 0)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose means will be calculated.
System.Int32[]	weights	A vector containing the importance of each sample in the matrix.
System.Int32	dimension	The dimension along which the means will be calculated. Pass 0 to compute a row vector containing the mean of each column, or 1 to compute a column vector containing the mean of each row. Default value is 0.

Returns

Type	Description
System.Double[]	Returns a vector containing the means of the given matrix.

View Source

WeightedMin(Double[], Double[], out Int32, Boolean)

Gets the minimum value in a vector of observations that has a weight higher than zero.

Declaration

public static double WeightedMin(this double[] values, double[] weights, out int imin, bool alreadySorted = false)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector values.
System.Double[]	weights	A vector containing the importance of each sample in .
System.Int32	imin	The index of the minimum element in the vector, or -1 if it could not be found.
System.Boolean	alreadySorted	Pass true if the list of values is already sorted.

Returns

Type	Description
System.Double	The minimum value in the given data.

View Source

WeightedMin(Double[], Int32[], out Int32, Boolean)

Gets the minimum value in a vector of observations that has a weight higher than zero.

Declaration

public static double WeightedMin(this double[] values, int[] weights, out int imin, bool alreadySorted = false)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector values.
System.Int32[]	weights	The number of times each sample should be repeated.
System.Int32	imin	The index of the minimum element in the vector, or -1 if it could not be found.
System.Boolean	alreadySorted	Pass true if the list of values is already sorted.

Returns

Type	Description
System.Double	The minimum value in the given data.

View Source

WeightedMode<T>(T[], Double[], Boolean, Boolean)

Computes the Mode of the given values.

Declaration

public static T WeightedMode<T>(this T[] values, double[] weights, bool inPlace = false, bool alreadySorted = false)

Parameters

Type	Name	Description
T[]	values	A number array containing the vector values.
System.Double[]	weights	The number of times each sample should be repeated.
System.Boolean	inPlace	True to perform the operation in place, altering the original input vector.
System.Boolean	alreadySorted	Pass true if the list of values is already sorted.

Returns

Type	Description
T	The most common value in the given data.

Type Parameters

Name	Description
T

View Source

WeightedMode<T>(T[], Int32[], Boolean, Boolean)

Computes the Mode of the given values.

Declaration

public static T WeightedMode<T>(this T[] values, int[] weights, bool inPlace = false, bool alreadySorted = false)

Parameters

Type	Name	Description
T[]	values	A number array containing the vector values.
System.Int32[]	weights	The number of times each sample should be repeated.
System.Boolean	inPlace	True to perform the operation in place, altering the original input vector.
System.Boolean	alreadySorted	Pass true if the list of values is already sorted.

Returns

Type	Description
T	The most common value in the given data.

Type Parameters

Name	Description
T

View Source

WeightedScatter(Double[][], Double[], Double[], Double, Int32)

Calculates the scatter matrix of a sample matrix.

Declaration

public static double[, ] WeightedScatter(this double[][] matrix, double[] weights, double[] means, double factor, int dimension)

Parameters

Type	Name	Description
System.Double[][]	matrix	A number multi-dimensional array containing the matrix values.
System.Double[]	weights	An unit vector containing the importance of each sample in . The sum of this array elements should add up to 1.
System.Double[]	means	The mean value of the given values, if already known.
System.Double	factor	A real number to multiply each member of the matrix.
System.Int32	dimension	Pass 0 to if mean vector is a row vector, 1 otherwise. Default value is 0.

Returns

Type	Description
System.Double[,]	The covariance matrix.

Remarks

By dividing the Scatter matrix by the sample size, we get the population Covariance matrix. By dividing by the sample size minus one, we get the sample Covariance matrix.

View Source

WeightedScatter(Double[][], Int32[], Double[], Double, Int32)

Calculates the scatter matrix of a sample matrix.

Declaration

public static double[, ] WeightedScatter(this double[][] matrix, int[] weights, double[] means, double factor, int dimension)

Parameters

Type	Name	Description
System.Double[][]	matrix	A number multi-dimensional array containing the matrix values.
System.Int32[]	weights	The number of times each sample should be repeated.
System.Double[]	means	The mean value of the given values, if already known.
System.Double	factor	A real number to multiply each member of the matrix.
System.Int32	dimension	Pass 0 to if mean vector is a row vector, 1 otherwise. Default value is 0.

Returns

Type	Description
System.Double[,]	The covariance matrix.

Remarks

By dividing the Scatter matrix by the sample size, we get the population Covariance matrix. By dividing by the sample size minus one, we get the sample Covariance matrix.

View Source

WeightedStandardDeviation(Double[], Double[])

Computes the Standard Deviation of the given values.

Declaration

public static double WeightedStandardDeviation(this double[] values, double[] weights)

Parameters

Type	Name	Description
System.Double[]	values	A double array containing the vector members.
System.Double[]	weights	An unit vector containing the importance of each sample in . The sum of this array elements should add up to 1.

Returns

Type	Description
System.Double	The standard deviation of the given data.

View Source

WeightedStandardDeviation(Double[], Double[], WeightType)

Computes the Standard Deviation of the given values.

Declaration

public static double WeightedStandardDeviation(this double[] values, double[] weights, WeightType weightType)

Parameters

Type	Name	Description
System.Double[]	values	A double array containing the vector members.
System.Double[]	weights	An unit vector containing the importance of each sample in .
WeightType	weightType	How the weights should be interpreted for the bias correction.

Returns

Type	Description
System.Double	The standard deviation of the given data.

View Source

WeightedStandardDeviation(Double[], Double[], Boolean, WeightType)

Computes the Standard Deviation of the given values.

Declaration

public static double WeightedStandardDeviation(this double[] values, double[] weights, bool unbiased, WeightType weightType)

Parameters

Type	Name	Description
System.Double[]	values	A double array containing the vector members.
System.Double[]	weights	An unit vector containing the importance of each sample in .
System.Boolean	unbiased	Pass true to compute the sample variance; or pass false to compute the population variance. For integers weights , the bias correction is equivalent to the non-weighted case. For fractional weights, the variance bias cannot be completely eliminated.
WeightType	weightType	How the weights should be interpreted for the bias correction.

Returns

Type	Description
System.Double	The standard deviation of the given data.

View Source

WeightedStandardDeviation(Double[], Double[], Double)

Computes the Standard Deviation of the given values.

Declaration

public static double WeightedStandardDeviation(this double[] values, double[] weights, double mean)

Parameters

Type	Name	Description
System.Double[]	values	A double array containing the vector members.
System.Double[]	weights	An unit vector containing the importance of each sample in . The sum of this array elements should add up to 1.
System.Double	mean	The mean of the vector, if already known.

Returns

Type	Description
System.Double	The standard deviation of the given data.

View Source

WeightedStandardDeviation(Double[], Double[], Double, Boolean, WeightType)

Computes the Standard Deviation of the given values.

Declaration

public static double WeightedStandardDeviation(this double[] values, double[] weights, double mean, bool unbiased, WeightType weightType = WeightType.Fraction)

Parameters

Type	Name	Description
System.Double[]	values	A double array containing the vector members.
System.Double[]	weights	An unit vector containing the importance of each sample in . The sum of this array elements should add up to 1.
System.Double	mean	The mean of the vector, if already known.
System.Boolean	unbiased	Pass true to compute the sample variance; or pass false to compute the population variance. For integers weights , the bias correction is equivalent to the non-weighted case. For fractional weights, the variance bias cannot be completely eliminated.
WeightType	weightType	How the weights should be interpreted for the bias correction.

Returns

Type	Description
System.Double	The standard deviation of the given data.

View Source

WeightedStandardDeviation(Double[], Int32[])

Computes the Standard Deviation of the given values.

Declaration

public static double WeightedStandardDeviation(this double[] values, int[] weights)

Parameters

Type	Name	Description
System.Double[]	values	A double array containing the vector members.
System.Int32[]	weights	A vector containing how many times each element in repeats itself in the non-weighted data.

Returns

Type	Description
System.Double	The standard deviation of the given data.

View Source

WeightedStandardDeviation(Double[], Int32[], Double)

Computes the Standard Deviation of the given values.

Declaration

public static double WeightedStandardDeviation(this double[] values, int[] weights, double mean)

Parameters

Type	Name	Description
System.Double[]	values	A double array containing the vector members.
System.Int32[]	weights	A vector containing how many times each element in repeats itself in the non-weighted data.
System.Double	mean	The mean of the vector, if already known.

Returns

Type	Description
System.Double	The standard deviation of the given data.

View Source

WeightedStandardDeviation(Double[], Int32[], Double, Boolean)

Computes the Standard Deviation of the given values.

Declaration

public static double WeightedStandardDeviation(this double[] values, int[] weights, double mean, bool unbiased)

Parameters

Type	Name	Description
System.Double[]	values	A double array containing the vector members.
System.Int32[]	weights	A vector containing how many times each element in repeats itself in the non-weighted data.
System.Double	mean	The mean of the vector, if already known.
System.Boolean	unbiased	Pass true to compute the sample variance; or pass false to compute the population variance. For integers weights , the bias correction is equivalent to the non-weighted case. For fractional weights, the variance bias cannot be completely eliminated.

Returns

Type	Description
System.Double	The standard deviation of the given data.

View Source

WeightedStandardDeviation(Double[][], Double[], Boolean)

Calculates the matrix Standard Deviations vector.

Declaration

public static double[] WeightedStandardDeviation(this double[][] matrix, double[] weights, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose deviations will be calculated.
System.Double[]	weights	The number of times each sample should be repeated.
System.Boolean	unbiased	Pass true to compute the standard deviation using the sample variance. Pass false to compute it using the population variance. See remarks for more details.

Returns

Type	Description
System.Double[]	Returns a vector containing the standard deviations of the given matrix.

Remarks

                      N
   σ² = 1 / (N - 1)  ∑   (x_i − μ)²
                      i=1

Setting unbiased to false will assume the given values already represent the whole population, and will compute the population variance using the formula:

                      N
   σ² =   (1 / N)    ∑   (x_i − μ)²
                      i=1

View Source

WeightedStandardDeviation(Double[][], Double[], Double[], Boolean)

Calculates the matrix Standard Deviations vector.

Declaration

public static double[] WeightedStandardDeviation(this double[][] matrix, double[] weights, double[] means, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose deviations will be calculated.
System.Double[]	weights	The number of times each sample should be repeated.
System.Double[]	means	The mean vector containing already calculated means for each column of the matrix.
System.Boolean	unbiased	Pass true to compute the standard deviation using the sample variance. Pass false to compute it using the population variance. See remarks for more details.

Returns

Type	Description
System.Double[]	Returns a vector containing the standard deviations of the given matrix.

Remarks

                      N
   σ² = 1 / (N - 1)  ∑   (x_i − μ)²
                      i=1

Setting unbiased to false will assume the given values already represent the whole population, and will compute the population variance using the formula:

                      N
   σ² =   (1 / N)    ∑   (x_i − μ)²
                      i=1

View Source

WeightedStandardDeviation(Double[][], Int32[], Boolean)

Calculates the matrix Standard Deviations vector.

Declaration

public static double[] WeightedStandardDeviation(this double[][] matrix, int[] weights, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose deviations will be calculated.
System.Int32[]	weights	The number of times each sample should be repeated.
System.Boolean	unbiased	Pass true to compute the standard deviation using the sample variance. Pass false to compute it using the population variance. See remarks for more details.

Returns

Type	Description
System.Double[]	Returns a vector containing the standard deviations of the given matrix.

Remarks

                      N
   σ² = 1 / (N - 1)  ∑   (x_i − μ)²
                      i=1

Setting unbiased to false will assume the given values already represent the whole population, and will compute the population variance using the formula:

                      N
   σ² =   (1 / N)    ∑   (x_i − μ)²
                      i=1

View Source

WeightedStandardDeviation(Double[][], Int32[], Double[], Boolean)

Calculates the matrix Standard Deviations vector.

Declaration

public static double[] WeightedStandardDeviation(this double[][] matrix, int[] weights, double[] means, bool unbiased = true)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose deviations will be calculated.
System.Int32[]	weights	The number of times each sample should be repeated.
System.Double[]	means	The mean vector containing already calculated means for each column of the matrix.
System.Boolean	unbiased	Pass true to compute the standard deviation using the sample variance. Pass false to compute it using the population variance. See remarks for more details.

Returns

Type	Description
System.Double[]	Returns a vector containing the standard deviations of the given matrix.

Remarks

                      N
   σ² = 1 / (N - 1)  ∑   (x_i − μ)²
                      i=1

Setting unbiased to false will assume the given values already represent the whole population, and will compute the population variance using the formula:

                      N
   σ² =   (1 / N)    ∑   (x_i − μ)²
                      i=1

View Source

WeightedStandardDeviation(Double[,], Double[])

Calculates the matrix Standard Deviations vector.

Declaration

public static double[] WeightedStandardDeviation(this double[, ] matrix, double[] weights)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose deviations will be calculated.
System.Double[]	weights	The number of times each sample should be repeated.

Returns

Type	Description
System.Double[]	Returns a vector containing the standard deviations of the given matrix.

View Source

WeightedStandardDeviation(Double[,], Double[], Double[])

Calculates the matrix Standard Deviations vector.

Declaration

public static double[] WeightedStandardDeviation(this double[, ] matrix, double[] weights, double[] means)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose deviations will be calculated.
System.Double[]	weights	The number of times each sample should be repeated.
System.Double[]	means	The mean vector containing already calculated means for each column of the matrix.

Returns

Type	Description
System.Double[]	Returns a vector containing the standard deviations of the given matrix.

View Source

WeightedStandardDeviation(Double[,], Int32[])

Calculates the matrix Standard Deviations vector.

Declaration

public static double[] WeightedStandardDeviation(this double[, ] matrix, int[] weights)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose deviations will be calculated.
System.Int32[]	weights	The number of times each sample should be repeated.

Returns

Type	Description
System.Double[]	Returns a vector containing the standard deviations of the given matrix.

View Source

WeightedStandardDeviation(Double[,], Int32[], Double[])

Calculates the matrix Standard Deviations vector.

Declaration

public static double[] WeightedStandardDeviation(this double[, ] matrix, int[] weights, double[] means)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose deviations will be calculated.
System.Int32[]	weights	The number of times each sample should be repeated.
System.Double[]	means	The mean vector containing already calculated means for each column of the matrix.

Returns

Type	Description
System.Double[]	Returns a vector containing the standard deviations of the given matrix.

View Source

WeightedVariance(Double[], Double[])

Computes the weighted Variance of the given values.

Declaration

public static double WeightedVariance(this double[] values, double[] weights)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector members.
System.Double[]	weights	An unit vector containing the importance of each sample in . The sum of this array elements should add up to 1.

Returns

Type	Description
System.Double	The variance of the given data.

View Source

WeightedVariance(Double[], Double[], WeightType)

Computes the weighted Variance of the given values.

Declaration

public static double WeightedVariance(this double[] values, double[] weights, WeightType weightType)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector members.
System.Double[]	weights	An unit vector containing the importance of each sample in .
WeightType	weightType	How the weights should be interpreted for the bias correction.

Returns

Type	Description
System.Double	The variance of the given data.

View Source

WeightedVariance(Double[], Double[], Boolean)

Computes the weighted Variance of the given values.

Declaration

public static double WeightedVariance(this double[] values, double[] weights, bool unbiased)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector members.
System.Double[]	weights	An unit vector containing the importance of each sample in . The sum of this array elements should add up to 1.
System.Boolean	unbiased	Pass true to compute the sample variance; or pass false to compute the population variance. For integers weights , the bias correction is equivalent to the non-weighted case. For fractional weights, the variance bias cannot be completely eliminated.

Returns

Type	Description
System.Double	The variance of the given data.

View Source

WeightedVariance(Double[], Double[], Boolean, WeightType)

Computes the weighted Variance of the given values.

Declaration

public static double WeightedVariance(this double[] values, double[] weights, bool unbiased, WeightType weightType)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector members.
System.Double[]	weights	An unit vector containing the importance of each sample in .
System.Boolean	unbiased	Pass true to compute the sample variance; or pass false to compute the population variance. For integers weights , the bias correction is equivalent to the non-weighted case. For fractional weights, the variance bias cannot be completely eliminated.
WeightType	weightType	How the weights should be interpreted for the bias correction.

Returns

Type	Description
System.Double	The variance of the given data.

View Source

WeightedVariance(Double[], Double[], Double)

Computes the weighted Variance of the given values.

Declaration

public static double WeightedVariance(this double[] values, double[] weights, double mean)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector members.
System.Double[]	weights	An unit vector containing the importance of each sample in . The sum of this array elements should add up to 1.
System.Double	mean	The mean of the array, if already known.

Returns

Type	Description
System.Double	The variance of the given data.

View Source

WeightedVariance(Double[], Double[], Double, Boolean, WeightType)

Computes the weighted Variance of the given values.

Declaration

public static double WeightedVariance(this double[] values, double[] weights, double mean, bool unbiased, WeightType weightType = WeightType.Fraction)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector members.
System.Double[]	weights	An unit vector containing the importance of each sample in .
System.Double	mean	The mean of the array, if already known.
System.Boolean	unbiased	Pass true to compute the sample variance; or pass false to compute the population variance. For integers weights , the bias correction is equivalent to the non-weighted case. For fractional weights, the variance bias cannot be completely eliminated.
WeightType	weightType	How the weights should be interpreted for the bias correction.

Returns

Type	Description
System.Double	The variance of the given data.

View Source

WeightedVariance(Double[], Int32[])

Computes the weighted Variance of the given values.

Declaration

public static double WeightedVariance(this double[] values, int[] weights)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector members.
System.Int32[]	weights	A vector containing how many times each element in repeats itself in the non-weighted data.

Returns

Type	Description
System.Double	The variance of the given data.

View Source

WeightedVariance(Double[], Int32[], Boolean)

Computes the weighted Variance of the given values.

Declaration

public static double WeightedVariance(this double[] values, int[] weights, bool unbiased)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector members.
System.Int32[]	weights	A vector containing how many times each element in repeats itself in the non-weighted data.
System.Boolean	unbiased	Pass true to compute the sample variance; or pass false to compute the population variance. For integers weights , the bias correction is equivalent to the non-weighted case. For fractional weights, the variance bias cannot be completely eliminated.

Returns

Type	Description
System.Double	The variance of the given data.

View Source

WeightedVariance(Double[], Int32[], Double)

Computes the weighted Variance of the given values.

Declaration

public static double WeightedVariance(this double[] values, int[] weights, double mean)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector members.
System.Int32[]	weights	A vector containing how many times each element in repeats itself in the non-weighted data.
System.Double	mean	The mean of the array, if already known.

Returns

Type	Description
System.Double	The variance of the given data.

View Source

WeightedVariance(Double[], Int32[], Double, Boolean)

Computes the weighted Variance of the given values.

Declaration

public static double WeightedVariance(this double[] values, int[] weights, double mean, bool unbiased)

Parameters

Type	Name	Description
System.Double[]	values	A number array containing the vector members.
System.Int32[]	weights	A vector containing how many times each element in repeats itself in the non-weighted data.
System.Double	mean	The mean of the array, if already known.
System.Boolean	unbiased	Pass true to compute the sample variance; or pass false to compute the population variance. For integers weights , the bias correction is equivalent to the non-weighted case. For fractional weights, the variance bias cannot be completely eliminated.

Returns

Type	Description
System.Double	The variance of the given data.

View Source

WeightedVariance(Double[][], Double[])

Calculates the matrix Variance vector.

Declaration

public static double[] WeightedVariance(this double[][] matrix, double[] weights)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose variances will be calculated.
System.Double[]	weights	An unit vector containing the importance of each sample in . The sum of this array elements should add up to 1.

Returns

Type	Description
System.Double[]	Returns a vector containing the variances of the given matrix.

View Source

WeightedVariance(Double[][], Double[], Double[])

Calculates the matrix Variance vector.

Declaration

public static double[] WeightedVariance(this double[][] matrix, double[] weights, double[] means)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose variances will be calculated.
System.Double[]	weights	An unit vector containing the importance of each sample in . The sum of this array elements should add up to 1.
System.Double[]	means	The mean vector containing already calculated means for each column of the matrix.

Returns

Type	Description
System.Double[]	Returns a vector containing the variances of the given matrix.

View Source

WeightedVariance(Double[][], Double[], Double[], Boolean, WeightType)

Calculates the matrix Variance vector.

Declaration

public static double[] WeightedVariance(this double[][] matrix, double[] weights, double[] means, bool unbiased, WeightType weightType = WeightType.Fraction)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose variances will be calculated.
System.Double[]	weights	An unit vector containing the importance of each sample in . The sum of this array elements should add up to 1.
System.Double[]	means	The mean vector containing already calculated means for each column of the matrix.
System.Boolean	unbiased	Pass true to compute the sample variance; or pass false to compute the population variance. For integers weights , the bias correction is equivalent to the non-weighted case. For fractional weights, the variance bias cannot be completely eliminated.
WeightType	weightType	How the weights should be interpreted for the bias correction.

Returns

Type	Description
System.Double[]	Returns a vector containing the variances of the given matrix.

View Source

WeightedVariance(Double[][], Int32[])

Calculates the matrix Variance vector.

Declaration

public static double[] WeightedVariance(this double[][] matrix, int[] weights)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose variances will be calculated.
System.Int32[]	weights	The number of times each sample should be repeated.

Returns

Type	Description
System.Double[]	Returns a vector containing the variances of the given matrix.

View Source

WeightedVariance(Double[][], Int32[], Double[])

Calculates the matrix Variance vector.

Declaration

public static double[] WeightedVariance(this double[][] matrix, int[] weights, double[] means)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose variances will be calculated.
System.Int32[]	weights	The number of times each sample should be repeated.
System.Double[]	means	The mean vector containing already calculated means for each column of the matrix.

Returns

Type	Description
System.Double[]	Returns a vector containing the variances of the given matrix.

View Source

WeightedVariance(Double[][], Int32[], Double[], Boolean)

Calculates the matrix Variance vector.

Declaration

public static double[] WeightedVariance(this double[][] matrix, int[] weights, double[] means, bool unbiased)

Parameters

Type	Name	Description
System.Double[][]	matrix	A matrix whose variances will be calculated.
System.Int32[]	weights	The number of times each sample should be repeated.
System.Double[]	means	The mean vector containing already calculated means for each column of the matrix.
System.Boolean	unbiased	Pass true to compute the sample variance; or pass false to compute the population variance. For integers weights , the bias correction is equivalent to the non-weighted case. For fractional weights, the variance bias cannot be completely eliminated.

Returns

Type	Description
System.Double[]	Returns a vector containing the variances of the given matrix.

View Source

WeightedVariance(Double[,], Double[])

Calculates the matrix Variance vector.

Declaration

public static double[] WeightedVariance(this double[, ] matrix, double[] weights)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose variances will be calculated.
System.Double[]	weights	An unit vector containing the importance of each sample in . The sum of this array elements should add up to 1.

Returns

Type	Description
System.Double[]	Returns a vector containing the variances of the given matrix.

View Source

WeightedVariance(Double[,], Double[], WeightType)

Calculates the matrix Variance vector.

Declaration

public static double[] WeightedVariance(this double[, ] matrix, double[] weights, WeightType weightType)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose variances will be calculated.
System.Double[]	weights	An unit vector containing the importance of each sample in .
WeightType	weightType	How the weights should be interpreted for the bias correction.

Returns

Type	Description
System.Double[]	Returns a vector containing the variances of the given matrix.

View Source

WeightedVariance(Double[,], Double[], Double[])

Calculates the matrix Variance vector.

Declaration

public static double[] WeightedVariance(this double[, ] matrix, double[] weights, double[] means)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose variances will be calculated.
System.Double[]	weights	An unit vector containing the importance of each sample in . The sum of this array elements should add up to 1.
System.Double[]	means	The mean vector containing already calculated means for each column of the matrix.

Returns

Type	Description
System.Double[]	Returns a vector containing the variances of the given matrix.

View Source

WeightedVariance(Double[,], Double[], Double[], WeightType)

Calculates the matrix Variance vector.

Declaration

public static double[] WeightedVariance(this double[, ] matrix, double[] weights, double[] means, WeightType weightType)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose variances will be calculated.
System.Double[]	weights	An unit vector containing the importance of each sample in . The sum of this array elements should add up to 1.
System.Double[]	means	The mean vector containing already calculated means for each column of the matrix.
WeightType	weightType	How the weights should be interpreted for the bias correction.

Returns

Type	Description
System.Double[]	Returns a vector containing the variances of the given matrix.

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WeightedVariance(Double[,], Double[], Double[], Boolean, WeightType)

Calculates the matrix Variance vector.

Declaration

public static double[] WeightedVariance(this double[, ] matrix, double[] weights, double[] means, bool unbiased, WeightType weightType = WeightType.Fraction)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose variances will be calculated.
System.Double[]	weights	An unit vector containing the importance of each sample in . How those values are interpreted depend on the value for `weightType`.
System.Double[]	means	The mean vector containing already calculated means for each column of the matrix.
System.Boolean	unbiased	Pass true to compute the sample variance; or pass false to compute the population variance. For integers weights , the bias correction is equivalent to the non-weighted case. For fractional weights, the variance bias cannot be completely eliminated.
WeightType	weightType	How the weights should be interpreted for the bias correction.

Returns

Type	Description
System.Double[]	Returns a vector containing the variances of the given matrix.

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WeightedVariance(Double[,], Int32[])

Calculates the matrix Variance vector.

Declaration

public static double[] WeightedVariance(this double[, ] matrix, int[] weights)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose variances will be calculated.
System.Int32[]	weights	The number of times each sample should be repeated.

Returns

Type	Description
System.Double[]	Returns a vector containing the variances of the given matrix.

View Source

WeightedVariance(Double[,], Int32[], Double[])

Calculates the matrix Variance vector.

Declaration

public static double[] WeightedVariance(this double[, ] matrix, int[] weights, double[] means)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose variances will be calculated.
System.Int32[]	weights	The number of times each sample should be repeated.
System.Double[]	means	The mean vector containing already calculated means for each column of the matrix.

Returns

Type	Description
System.Double[]	Returns a vector containing the variances of the given matrix.

View Source

WeightedVariance(Double[,], Int32[], Double[], Boolean)

Calculates the matrix Variance vector.

Declaration

public static double[] WeightedVariance(this double[, ] matrix, int[] weights, double[] means, bool unbiased)

Parameters

Type	Name	Description
System.Double[,]	matrix	A matrix whose variances will be calculated.
System.Int32[]	weights	The number of times each sample should be repeated.
System.Double[]	means	The mean vector containing already calculated means for each column of the matrix.
System.Boolean	unbiased	Pass true to compute the sample variance; or pass false to compute the population variance. For integers weights , the bias correction is equivalent to the non-weighted case. For fractional weights, the variance bias cannot be completely eliminated.

Returns

Type	Description
System.Double[]	Returns a vector containing the variances of the given matrix.